Chapter 9.6, Problem 6MRE

To determine

To find:the solution of the given equation by simplifying the equation.

Answer to Problem 6MRE

The equation can be written as ${\text{16st}}^{\text{3}}$ .

Explanation of Solution

Given:

  ${\left({\text{-2t}}^{\text{2}}\right)}^{\text{2}}\text{.}\frac{\text{4s}}{\text{t}}$ .

Concept used:

Two power of the given number multiply each other.

In the elimination method:

Either add or subtract equation to get an equation in one variable.

When the coefficients in one variable are opposites then add the equations to eliminate the variable and when the coefficients of one variable are equal and subtract the equation to eliminate a variable.

Calculation:

According to the given equation:

  ${\left({\text{-2t}}^{\text{2}}\right)}^{\text{2}}\text{.}\frac{\text{4s}}{\text{t}}$ .

Solving bracket term first and distributing the exponent and simplify:

  ${\left(\text{-2}\right)}^{\text{2}}{\left({\text{t}}^{\text{2}}\right)}^{\text{2}}\text{.}\frac{\text{4s}}{\text{t}}$ .

Multiplying the exponent and simplify:

  $\frac{{\text{16st}}^{\text{4}}}{\text{t}}$ .

Cancelling the common t from both numerator and denominator.

  ${\text{16st}}^{\text{4-1}}{\text{=16st}}^{\text{3}}$ .

Hence, the equation can be written as ${\text{16st}}^{\text{3}}$ .