Question

7^7 •(3^4)^3 __________ 21^9. show your work!

Answer 1

The exponential to simplify is:

$\frac{7^7(3^4)^3}{21^9}$

Let's use the property

$(a^m)^n=a^{mn}$

To simplify the numerator. So, we have:

$\frac{7^73^{12}}{21^9}$

Now, let's use the property:

$(a\cdot b)^n=a^nb^n^{}$

to simplify the denominator. Thus, we have:

$\begin{gathered} \frac{7^73^{12}}{21^9} \\ =\frac{7^73^{12}}{(3\cdot7)^9} \\ =\frac{7^73^{12}}{3^97^9} \end{gathered}$

Now, we can cross-out numerator and denominator and simplify. The steps are shown below:

$\begin{gathered} \frac{7^73^{12}}{3^97^9} \\ =7^{7-9}3^{12-9} \\ =7^{-2}3^3 \\ =\frac{3^3}{7^2} \\ =\frac{27}{49} \end{gathered}$