Chapter 8.3, Problem 12MRE

To determine

To calculate: The simplified form of ${\left(2y^3\right)}^3$ ,

where $x=2,y=1,a=-3,b=4$ .

Answer to Problem 12MRE

The simplified form of ${\left(2y^3\right)}^3$ is $8$ .

Explanation of Solution

Given information:

The statement “ ${\left(2y^3\right)}^3$ .”

Formula used:

When two or more functions are in the form of exponents then the formula used:

  ${\left(a^2\right)}^2=a^4$

The power of the exponent multiplied here.

Consider the provided statement “ ${\left(2y^3\right)}^3$ .”

Recall thatWhen two or more functions are in the form of exponents then the formula used:

  ${\left(a^2\right)}^2=a^4$

The power of the exponent multiplied here.

So, the given expression can be simplified as,

  ${\left(2y^3\right)}^3$

Put the values of $x=2,y=1,a=-3,b=4$ as given in the question,

Observe that on the equation no $a,b$ variables found, so put the value of $x,y$ only in the function ,

Now put the value of $x,y$ .

  $\begin{array}{c}{\left(2y^3\right)}^3={\left(2\cdot 1^3\right)}^3\\ ={\left(2\right)}^3\\ =8\end{array}$

Since, $8$ cannot be simplified further,

Hence, the simplified form of ${\left(2y^3\right)}^3$ is $8$ .