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Select the equivalent expression.

((4^(3))/(5^(-2)))^(5)=?
Choose 1 answer:
(A) 
(4^(8))/(5^(3))
(B) 
(4^(15))/(5^(10))
(C) 
4^(15)*5^(10)

Select the equivalent expression.\newline(4352)5=\left(\frac{4^{3}}{5^{-2}}\right)^{5}=?\newlineChoose 11 answer:\newline(A) 4853\frac{4^{8}}{5^{3}}\newline(B) 415510\frac{4^{15}}{5^{10}}\newline(C) 4155104^{15}\cdot 5^{10}

Full solution

Q. Select the equivalent expression.\newline(4352)5=\left(\frac{4^{3}}{5^{-2}}\right)^{5}=?\newlineChoose 11 answer:\newline(A) 4853\frac{4^{8}}{5^{3}}\newline(B) 415510\frac{4^{15}}{5^{10}}\newline(C) 4155104^{15}\cdot 5^{10}
  1. Apply power rule: Apply the power of a power rule.\newlineThe power of a power rule states that (am)n=amn(a^{m})^{n} = a^{m*n}. We will apply this rule to both the numerator and the denominator separately.\newline(4352)5=435525\left(\frac{4^{3}}{5^{-2}}\right)^{5} = \frac{4^{3*5}}{5^{-2*5}}
  2. Calculate exponents: Calculate the exponents.\newlineNow we will multiply the exponents.\newline43×5=4154^{3\times5} = 4^{15}\newline52×5=5105^{-2\times5} = 5^{-10}
  3. Simplify with negative exponent: Simplify the expression with negative exponent.\newlineA negative exponent means that the base is on the wrong side of the fraction line, so you flip the base to the other side. Therefore, 5105^{-10} becomes 1/(510)1/(5^{10}).\newline(415)/(510)=415×(510)(4^{15})/(5^{-10}) = 4^{15} \times (5^{10})
  4. Write final expression: Write the final expression.\newlineThe final expression is 415×5104^{15} \times 5^{10}, which corresponds to one of the answer choices.

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