Question

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

Answer 1

The exponential to simplify is:

`(7^7(3^4)^3)/(21^9)`

Let's use the property

`(a^m)^n=a^(mn)`

To simplify the numerator. So, we have:

`(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} (7^73^(12))/(21^9) \\ =(7^73^(12))/((3\cdot7)^9) \\ =(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} (7^73^(12))/(3^97^9) \\ =7^(7-9)3^(12-9) \\ =7^(-2)3^3 \\ =(3^3)/(7^2) \\ =(27)/(49) \end{gathered}`