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mathematics
basic technical mathematics
Questions and Answers of
Basic Technical Mathematics
Express each expression in simplest form with only positive exponents.2x(x − 1)−2 − 2(x2 + 1)(x − 1)−3
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. √√5√3 6-543 – 40a
Express each expression in simplest form with only positive exponents. (9a)⁰ (4x2) 1/3 (3b¹/2)] (26⁰)² “
Express each of the given expressions in simplest form with only positive exponents.2x−3 + 4y−2
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. 9 12
Simplify the given expressions. Express all answers with positive exponents.x5/6 x−1/3
Perform the indicated operations, expressing answers in simplest form with rationalized denominators. √23/3
Express each of the given expressions in simplest form with only positive exponents.a−1 + b−1
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √132M²N3
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable. 2√15 + √3 √15 - 2√3
Simplify the given expressions. Express all answers with positive exponents.m1/3m1/2
Express each expression in simplest form with only positive exponents.(W2 − 2WH + H2)−1/2
Perform the indicated operations, expressing answers in simplest form with rationalized denominators. 7 3
Use a calculator to evaluate each expression.17.981/4
Evaluate the given expressions.−32−4/5
Express each expression in simplest form with only positive exponents.7(1000)−2/3
Express each of the given expressions in simplest form with only positive exponents.(32 × 4−3)3
Express each radical in simplest form, rationalize denominators, and perform the indicated operations.√18y − 3√8y
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable. 4a-1/263/4 6-2 6-1 2a
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √80RSTV4
Perform the indicated operations, expressing answers in simplest form with rationalized denominators. √72 2
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. 4√2n² - √50n²
Evaluate the given expressions.64−2/3
Express each expression in simplest form with only positive exponents.8(400−3/2)
Express each of the given expressions in simplest form with only positive exponents.50 × 5−3
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. 2√31²-3√12t²
Evaluate the given expressions.16−7/4
Express each expression in simplest form with only positive exponents.322/5
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.√75ab2
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. √7 + √36 + 27
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.2(3√5)3
Express each of the given expressions in simplest form with only positive exponents.n−6/m−4
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable.(2x + 3)1/2 + (x +
Express each expression in simplest form with only positive exponents. -5х0 Зу-1
Evaluate the given expressions.8−2/3
Express each expression in simplest form with only positive exponents.3(25)3/2
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable. √27a4b³ 3
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.√x4y3z7
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.(4√3)2
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. √5 + √16 + 4
Perform the indicated operations, expressing answers in simplest form with rationalized denominators. $/45/16
Express each of the given expressions in simplest form with only positive exponents.x5/y−2
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable.2√2(3√10 − √6)
Perform the indicated operations, expressing answers in simplest form with rationalized denominators. 3/43/2
Evaluate the given expressions.−165/4
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.√pq2r7
Express each of the given expressions in simplest form with only positive exponents.t−8/t−3
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable. 3- 2√2 2√x
Evaluate the given expressions.1003/2
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.√x2y5
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable.
Express each of the given expressions in simplest form with only positive exponents.c7/c−2
Express each radical in simplest form, rationalize denominators, and perform the indicated operations.√32 + 5√24 − √54
Evaluate the given expressions.1252/3
Express each expression in simplest form with only positive exponents.(2c)−1z−2
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.√98
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.√7√35
Express each of the given expressions in simplest form with only positive exponents.5ss−5
Express each radical in simplest form, rationalize denominators, and perform the indicated operations.2√18 − √27 + √50
Evaluate the given expressions.811/4
Express each expression in simplest form with only positive exponents.8x−3y0
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.√108
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.√2√6
Express each of the given expressions in simplest form with only positive exponents.2a2a−6
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable.(√2x − 3√y)2
Determine each of the following as being either true or false. If it is false, explain it why. 1 √√3-√√2 √3+ √2
Express each radical in simplest form, rationalize denominators, and perform the indicated operations.8√6 − √12 − 5√6
Evaluate the given expressions.271/3
Determine each of the following as being either true or false. If it is false, explain it why.√5√7 = √35
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.√40
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.√2√51
Express each of the given expressions in simplest form with only positive exponents.y9y−2
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable.(2x−1 + y−2)−1
Express each radical in simplest form, rationalize denominators, and perform the indicated operations.√28 + √5 − 3√7
Simplify the resulting expressions if the given changes are made in the indicated examples of this section.In Example 9, replace b−2 with b−4 and then find the resulting expression.Data from
Evaluate the given expressions.361/2
Perform the indicated operations on the resulting expressions if the given changes are made in the indicated examples of this section.In Example 6, rationalize the numerator of the given
Solve the resulting problems if the given changes are made in the indicated examples of this section.In Example 9, change the sign in the numerator from − to + and then find the result.Data from
Solve the resulting problems if the given changes are made in the indicated examples of this section.In Example 7(d), change the exponent −1/2 to −3/2.Data from Example 7(d) (4x4)-1/2-3x-3
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.√75
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.√5√7
Express each of the given expressions in simplest form with only positive exponents.x8x−3
Solve the resulting problems if the given changes are made in the indicated examples of this section.In Example 6, change the exponent to −1/3.Data from Example 6Plot the graph of the function y =
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable.2√20 − √125
Express each radical in simplest form, rationalize denominators, and perform the indicated operations.8√11 − 3√11
Simplify the resulting expressions if the given changes are made in the indicated examples of this section.In Example 7(b), change the root to a fourth root and then find the resulting
Determine each of the following as being either true or false. If it is false, explain it why.√48 − √27 = √3
Determine each of the following as being either true or false. If it is false, explain it why. (16-1/2) (12) 4- = 2
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable.(as−1/3t3/4)12
Express each radical in simplest form, rationalize denominators, and perform the indicated operations.3√7 + 5√7
Sketch the appropriate curves. A calculator may be used.The height h (in m) of a certain rocket ascending vertically is given by h = 800 tanθ, where θ is the angle of elevation from an observer 800
Display the graphs of the given functions on a calculator. y = 2 cos 4x cos(x - - cos(x-4)
Perform the indicated operations on the resulting expressions if the given changes are made in the indicated examples of this section.In Example 5, change the sign in the denominator from − to +
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable. 1003/2 8-2/3
Solve the resulting problems if the given changes are made in the indicated examples of this section.In Example 8(b), change the 3−1 in the denominator to 3−2 and then find the result.Data from
Determine each of the following as being either true or false. If it is false, explain it why. 9 = + +91/
Simplify the resulting expressions if the given changes are made in the indicated examples of this section.In Example 4, changeand then find the resulting simplified expression.Data from Example 4
Solve the resulting problems if the given changes are made in the indicated examples of this section.In Example 4(b), change the exponent to −3/2.Data from Example 4(b)We note in (b) that Eq.
Perform the indicated operations on the resulting expressions if the given changes are made in the indicated examples of this section.In Example 4(a), change √5 to 6√5 and then perform the
Solve the resulting problems if the given changes are made in the indicated examples of this section.In Example 6, change the term 2a to 2a–1 and then find the result.Data from Example 6(a)(b) (2a
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