Question

What is the cube root of b^27?
a. b^3
b. b^9
c. b^18
d. b^34

Answer 1

Option b is correct.

Explanation:

`\sqrt[3]{b^(27) }) =(b^(27)) ^{(1)/(3) } =b^((27)/(3) )= b^9\\`

Explanation in words

We can write any radical form in to exponent form therefore we wrote

cube root in to exponent form as
`(1)/(3)`

In second step we used the formula for exponent of exponent of terms

which gives 27 divided by 3 in the exponent of b consequently we get

9 in the exponent of b or we can write
`b^9` which gives option b as the answer.

Answer 2

Answer: b. b^9

Explanation:

1. You can rewrite
`\sqrt[3]{b^(27)}` as following:

`(b^(27))^{(1)/(3)}`

Because, by definition
`\sqrt[n]{x}=x^{(1)/(n)}`

2. Now, keeping on mind the exponents properties, you can multiply the exponents, then you obtain:

`b^{(27)/(3)}`

3. Finally, you must simplify the exponent, then, you obtain the following result:

`b^(9)`