Chapter 1.2, Problem 5STP

Solve each exercise and enter your answer on the grid provided. Round your answers to the nearest hundredth if necessary.

What is the value of ${\left(5x^2\right)}^3+16y÷4y$ for $x=2$ and $y=3?$

To determine

To find: the value of ${\left(5x^2\right)}^3+16y÷4y$ for $x=2$ and $y=3$ .

Answer to Problem 5STP

  $8004$

Explanation of Solution

Given:

The expression ${\left(5x^2\right)}^3+16y÷4y$

Substitute $x=2$ and $y=3$ in ${\left(5x^2\right)}^3+16y÷4y$ ,

  ${\left(5x^2\right)}^3+16y÷4y={\left(5{\left(2\right)}^2\right)}^3+16\left(3\right)÷4\left(3\right)$

To simplify the expression ${\left(5{\left(2\right)}^2\right)}^3+16\left(3\right)÷4\left(3\right)$ , rules of order of operations are to be followed.

According to it, first parenthesis is solve, then exponent, then division, then multiplication, then addition and lastly subtraction.

So, here first solve the parenthesis and in parenthesis first solve the exponent then multiply,

  $\begin{array}{c}{\left(5{\left(2\right)}^2\right)}^3+16\left(3\right)÷4\left(3\right)={\left(5\times 4\right)}^3+16\left(3\right)÷4\left(3\right)\\ ={\left(20\right)}^3+48÷12\end{array}$

Now, solve the exponent,

  $\begin{array}{c}{\left(5{\left(2\right)}^2\right)}^3+16\left(3\right)÷4\left(3\right)={\left(20\right)}^3+48÷12\\ =8000+48÷12\end{array}$

Now perform the division,

  $\begin{array}{c}{\left(5{\left(2\right)}^2\right)}^3+16\left(3\right)÷4\left(3\right)=8000+48÷12\\ =8000+4\end{array}$

Lastly perform the addition,

  $\begin{array}{c}{\left(5{\left(2\right)}^2\right)}^3+16\left(3\right)÷4\left(3\right)=8000+4\\ =8004\end{array}$