Question

the square shown has sides of length $7z^{6}$ decimeters. find its area. the area of the square is equal to \square square decimeters. (simplify your answer.)

Explanation:

Step1: Recall the formula for the area of a square

The area \( A \) of a square is given by the formula \( A = s^2 \), where \( s \) is the length of a side.

Step2: Substitute the given side length into the formula

Here, the side length \( s = 7z^6 \) decimeters. So we need to square \( 7z^6 \), which means \( (7z^6)^2 \).

Step3: Apply the power of a product rule \((ab)^n=a^n b^n\)

\((7z^6)^2 = 7^2\times (z^6)^2\)

Step4: Simplify the exponents

We know that \( 7^2 = 49 \) and by the power of a power rule \((a^m)^n=a^{m\times n}\), so \((z^6)^2 = z^{6\times2}=z^{12}\).

Step5: Combine the results

Multiplying the two simplified parts together, we get \( 49z^{12} \).

Answer:

\( 49z^{12} \)