Chapter 7.4, Problem 3STP

For Exercises $1-6,$ choose the correct letter.

A fraction reduces to 36. If its numerator is ${(6x)}^5,$ what is its denominator?

A. $6^{3}x$

B. $6^3{x}^5$

C. $6x^5$

D. $6^7{x}^5$

To determine

To determine the denominator for the given condition.

Answer to Problem 3STP

Option B is correct.

Explanation of Solution

Given information:

A fraction reduces to 36.

Numerator is ${\left(6x\right)}^5$

Let the denominator be y .

Hence according to question we get,

  $\begin{array}{l}36=\frac{{\left(6x\right)}^5}{y}\\ 36y=6^5{x}^5\\ 6^{2}y=6^5{x}^5\\ y=6^3{x}^5\end{array}$

Hence B is the correct option.