Chapter 1.6, Problem 64HP

To determine

To find: an expression equivalent to ${\left(\frac{3x^3}{y}\right)}^3$ .

Answer to Problem 64HP

The answer is none.

Explanation of Solution

Given information:

Given options are,

F. $\frac{9x^6}{3y}$

G. $\frac{9x^9}{y^3}$

H. $\frac{27x^6}{3y}$

I. $\frac{27x^9}{y^3}$ .

Calculation:

Useful statements,

  ${\left(x^a\right)}^b=x^{a\cdot b}\text{and}{\left(x\cdot y\right)}^a=x^a\cdot y^a$

Third power is entering brackets on each number and variable.

The rewrite given identity will get

  $\begin{array}{c}{3}^3\cdot {\left(x^3\right)}^3\cdot {\left(\frac{1}{y^3}\right)}^3=3^3.{\left(x^3\right)}^3\cdot {\left(y^{-3}\right)}^3\\ =27\cdot x^9\cdot y^{-9}\\ =\frac{27x^9}{y^9}\end{array}$

There is no valid answer is given.

So, the answer is none.