Question

Use the power rules for exponents to simplify the expression.
left parenthesis six sevenths right parenthesis Superscript 5
times6 squared

Answer 1

To simplify the expression \(\left(\frac{6}{7}\right)^5 \times 6^2\), we can first calculate each part separately and then combine them.

1. Calculate \(\left(\frac{6}{7}\right)^5\):

\[
\left(\frac{6}{7}\right)^5 = \frac{6^5}{7^5}
\]

2. Calculate \(6^2\):

\[
6^2 = 36
\]

3. Now combine the two results:

\[
\left(\frac{6}{7}\right)^5 \times 6^2 = \frac{6^5}{7^5} \times 36
\]

Since \(36 = 6^2\), we can express the multiplication as:

\[
\frac{6^5 \times 6^2}{7^5}
\]

4. Use the power rule for exponents which states that \(a^m \times a^n = a^{m+n}\):

\[
\frac{6^{5+2}}{7^5} = \frac{6^7}{7^5}
\]

The simplified expression is:

\[
\frac{6^7}{7^5}
\]