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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Simplify the resulting expressions if the given changes are made in the indicated examples of this section.In Example 5(d), change the 8 to 27 and then find the resulting expression.Data from Example
Simplify the resulting expressions if the given changes are made in the indicated examples of this section.In Example 3(a), change 27 to 45 and then find the resulting simplified expression.Data from
Solve the resulting problems if the given changes are made in the indicated examples of this section.In Example 2, change the exponent to 4/3.Data from Example 2 82/3 = 3√/82 (38)² = (2)² = 4 or
Perform the indicated operations on the resulting expressions if the given changes are made in the indicated examples of this section.In Example 2(a), change 4√2 to 4√8 and then perform the
Simplify the resulting expressions if the given changes are made in the indicated examples of this section.In Example 4(b), change the exponent of b to 4 and then find the resulting expression.Data
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable.(3πx−4)−2
Determine each of the following as being either true or false. If it is false, explain why.2x0 = 1
Solve the resulting problems if the given changes are made in the indicated examples of this section.In Example 3, change the factor x2 to x−2 and then find the result.Data from Example 3(a)(b)In
Simplify the given expressions. For those with exponents, express each result with only positive exponents. For the radicals, rationalize the denominator where applicable.−5y0
Express each expression in simplest form with only positive exponents. -2
Expressin simplest radical form with a rationalized denominator. 3-1/2 2
Express each radical in simplest form, rationalize denominators, and perform the indicated operations.√27x + 3√18x
Express each of the given expressions in simplest form with only positive exponents.(2πx−1)2
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.√3(√6 − √5)
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.3√16
Evaluate the given expressions.51/253/2
Express each expression in simplest form with only positive exponents. 2x3 3 -3
Express each radical in simplest form, rationalize denominators, and perform the indicated operations.2√28 + 3√175
In the study of fluid flow in pipes, the expression 0.220N−1/6 is found. Evaluate this expression for N = 64 × 106.
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. √100+25 7√80
Express each of the given expressions in simplest form with only positive exponents.(3xy−2)3
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.3√5(√15 − 2√5)
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. 3√200√162 - √288
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.4√48
Express each expression in simplest form with only positive exponents. -82/3 49-1/2
Evaluate the given expressions.(44)3/2
Express each of the given expressions in simplest form with only positive exponents.2(5an−2)−1
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.(2 − √5)(2 + √5)
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.5√96
Evaluate the given expressions.(36)2/3
Express each of the given expressions in simplest form with only positive exponents.4(6s2t−1)−2
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.4(1 − √7)2
Express each expression in simplest form with only positive exponents. 4-45 2-90
Evaluate the given expressions. 121-1/2 100/2
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.3√−512
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. 2√44 √99 + √2√88
Evaluate the given expressions. 10001/3 -400-1/2
Express each of the given expressions in simplest form with only positive exponents.(−4)0
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. 3√/25a¹b²
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. 3√75R+ 2√48R - 2√18R
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.(√30 − 2√3)(√30 + 7√3)
Evaluate the given expressions. -7-1/2 6-171/2
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.3√8a2
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. 2√28 √108-6√175
Express each expression in simplest form with only positive exponents.(2a2/3b1/6)6
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √64r³s4t5
Express each of the given expressions in simplest form with only positive exponents.−40
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.(3√7a − √50)(√7a + √2)
Express each expression in simplest form with only positive exponents.(ax−1/2y1/4)8
Evaluate the given expressions. 152/3 5215-1/3
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. √40 + √
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √√/16x³y³z¹1
Evaluate the given expressions. (-27)4/3 6
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. E t8re
Express each of the given expressions in simplest form with only positive exponents.−9x0
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.(3√11 − √x)(2√11 + 5√x)
Express each expression in simplest form with only positive exponents.(−32m15n10)3/5
Express each of the given expressions in simplest form with only positive exponents.(−7x)0
Evaluate the given expressions. (-8) 2/3 -2
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. 25 { + - - 4/18 2
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.(2√10 + 3√15)(√10 − 7√15)
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. 一冷k
Express each expression in simplest form with only positive exponents.(27x−6y9)2/3
Perform the indicated operations, expressing answers in simplest form with rationalized denominators. √3x (2√3x - √√xy)
Express each of the given expressions in simplest form with only positive exponents.3x−2
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.√a(√ab + √c3)
Express each expression in simplest form with only positive exponents.6L−2 − 4C−1
Express each of the given expressions in simplest form with only positive exponents.(3x)−2
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator.7√47√64
Evaluate the given expressions. -4-1/2 (-64)-4/3
Perform the indicated operations, expressing answers in simplest form with rationalized denominators. √6-9 ୨୮
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. ˋㄧˋㄧㄣ
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. PP²v 2
Perform the indicated operations, expressing answers in simplest form with rationalized denominators. 5-√10 /10
Express each expression in simplest form with only positive exponents. 3x-1 3x-1 + y-1
Express each expression in simplest form with only positive exponents.C4C−1 + (C4)−1
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √3m³n8 √9mn
Express each expression in simplest form with only positive exponents. 9a (2a)-¹ a
Express each of the given expressions in simplest form with only positive exponents.(7a−1x)−3
Express each of the given expressions in simplest form with only positive exponents. ( 3 -4
Evaluate the given expressions.125−2/3 − 100−3/2
Express each radical in simplest form, rationalize denominators, and perform the indicated operations.3√81 + 3√3000
Express each of the given expressions in simplest form with only positive exponents.7a−1x−3
Express each of the given expressions in simplest form with only positive exponents. 3 -2 -3.
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. 2
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. 2
Evaluate the given expressions.320.4 + 25−0.5
Express each radical in simplest form, rationalize denominators, and perform the indicated operations.3√−16 + 3√54
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. √₂ 213
Express each of the given expressions in simplest form with only positive exponents. 6-2 -3
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.(√x − 4√y)2
Express each expression in simplest form with only positive exponents.(a − 3b−1)−1
Express each radical in simplest form, rationalize denominators, and perform the indicated operations.4√32 − 8√4
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.(√c + √5d)(√c − √5d)
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. 5√ab – √4abs
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. 3 ୯
Express each of the given expressions in simplest form with only positive exponents. 5 2n-2₁-2 D-1
Express each expression in simplest form with only positive exponents.(2s−2 + t)−2
Use a calculator to evaluate each expression.(−750.81)2/3
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. 12

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