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Can you explain to me how to solve this please

Can you explain to me how to solve this please-example-1
User Fluxsaas
by
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1 Answer

4 votes

To solve the exercise you can use the following properties of exponents and radicals


a^{(m)/(n)}=\sqrt[n]{a^m}
a^ma^n=a^(m+n)
(a^m)/(a^n)=a^(m-n)

So, you have


\begin{gathered} \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=\frac{7^{(1)/(3)}\cdot7^{(1)/(2)}}{\sqrt[6]{7^5}} \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=\frac{7^{(1)/(3)+(1)/(2)}}{7^{(5)/(6)}} \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=\frac{7^{(5)/(6)}}{7^{(5)/(6)}} \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=7^{(5)/(6)-(5)/(6)} \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=7^0 \end{gathered}

By definition


\begin{gathered} a^0=1 \\ \text{Where a }\\e0 \end{gathered}

So


\begin{gathered} \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=7^0 \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=1 \end{gathered}

Therefore, the correct answer is b. 1.

User Ekeko
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7.0k points