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

​
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:

$$\boxed{{\displaystyle 7}}$$