Question

The expression cube root of, 7, end cube root, dot, cube root of, 7, squared, end cube root
3

7
​
⋅
3

7
2

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


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:

\[
\boxed{7}
\]