The expression cube root of, 7, end cube root, dot, cube root of, 7, squared, end cube root

Question

3

7
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⋅
3

7
2

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is equivalent to
Answer
Multiple Choice Answers
7, start superscript, start fraction, 9, divided by, 2, end fraction, end superscript7
2
9
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7, start superscript, start fraction, 2, divided by, 9, end fraction, end superscript7
9
2
​


77
7, squared7
2

Answer 1

To simplify the expression \(\sqrt[3]{7} \cdot \sqrt[3]{7^2}\), we can use the property of exponents that states \(\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a \cdot b}\).

In this case:

\[ \sqrt[3]{7} \cdot \sqrt[3]{7^2} = \sqrt[3]{7 \cdot 7^2} = \sqrt[3]{7^{1+2}} = \sqrt[3]{7^3} \]

Now, we simplify \(\sqrt[3]{7^3}\):

\[ \sqrt[3]{7^3} = 7 \]

Thus, the expression \(\sqrt[3]{7} \cdot \sqrt[3]{7^2}\) simplifies to \(7\).

So, the answer is:

\[ \boxed{7} \]