Questions: Perform the exponentiation by hand. Then use a calculator to check your work. [ left(frac49right)^2 ] (Simplify your answer.)

$Perform the exponentiation by hand. Then use a calculator to check your work. [ left(frac49right)^2 ] (Simplify your answer.)$

Transcript text: Perform the exponentiation by hand. Then use a calculator to check your work. \[ \left(\frac{4}{9}\right)^{2} \] $\square$ (Simplify your answer.)

Solution

Solution Steps

To solve the problem of exponentiating the fraction $\left(\frac{4}{9}\right)^{2}$, we need to raise both the numerator and the denominator to the power of 2. This means calculating $4^2$ and $9^2$ separately, and then forming a new fraction with these results. Finally, we simplify the fraction if possible.

Step 1: Calculate the Square of the Numerator

To find $\left(\frac{4}{9}\right)^{2}$, we first calculate the square of the numerator: \[ 4^2 = 16 \]

Step 2: Calculate the Square of the Denominator

Next, we calculate the square of the denominator: \[ 9^2 = 81 \]

Step 3: Form the New Fraction

Using the results from the previous steps, we form the new fraction: \[ \frac{16}{81} \]

Step 4: Simplify the Fraction

The fraction $\frac{16}{81}$ is already in its simplest form, as 16 and 81 have no common factors other than 1.