Chapter A3, Problem 1CP

Checkpoint 1 Worked-out solution available at LarsonAppliedCalculus.com

Evaluate $y=4x^{-2}\text{ for }x=3$.

To determine

To calculate: The value of expression $y=4x^{-2}$ for $x$ equal to $3$.

Answer to Problem 1CP

Solution:

The value of the given expression is $\underset{\_}{\frac{4}{9}}$.

Explanation of Solution

Given Information:

The expression is $y=4x^{-2}$.

Formula used:

Use the property of negative exponent,

$x^{-n}=\frac{1}{x^n}$

Calculation:

The exponent expression is, $y=4x^{-2}$

Substitute $3$ for $x$ in the above expression.

$\begin{array}{c}y=4x^{-2}\\ =4{\left(3\right)}^{-2}\end{array}$

Now, from the property of negative exponent.

$\begin{array}{c}y=4{\left(\frac{1}{3}\right)}^2\\ =\frac{4}{9}\end{array}$

Hence, the value of the provided expression for $x$ equal to 3 is $\frac{4}{9}$.