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

User Schmittsfn
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1 Answer

25 votes
25 votes

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}

User Bjw
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