Question

Evaluate each expression if $\mathbf{a}\mathbf{=}\mathbf{-}\mathbf{9}\mathbf{,}\mathbf{b}\mathbf{=}\frac{\mathbf{2}}{\mathbf{3}}\mathbf{,}\mathbf{c}\mathbf{=}\mathbf{8}\mathbf{,}$and $\mathbf{d}\mathbf{=}\mathbf{-}\mathbf{6}$.

8. $\frac{\mathbf{a}}{{\mathbf{b}}^{\mathbf{2}}}\mathbf{+}\mathbf{c}$

Short answer

The value of $\frac{a}{b^2}+c$ is $\mathbf{-}\mathbf{12}\mathbf{.}\mathbf{25}$.

Step-by-step solution

– Description of step.

Substitute $\frac{2}{3}$for b into $b^2$.

${\left(\frac{2}{3}\right)}^2=\frac{4}{9}$

– Description of step.

Substitute $\frac{4}{9}$for $b^2$, $-9$ for a and 8 for c.

$\frac{-9}{\left(\frac{4}{9}\right)}+8=\frac{-81}{4}+8$

– Description of step.

Simplify the expression obtained in step 2.

$\begin{array}{c}\frac{-81+32}{4}=\frac{-49}{4}\\ =-12.25\end{array}$

Therefore, the value of $\frac{a}{b^2}+c$ is $-12.25$.