Question

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

Answer 1

Answer:

Option b is correct.

Step-by-step explanation:

$\sqrt[3]{b^{27} }) =(b^{27}) ^{\frac{1}{3} } =b^(\frac{27}{3} )= b^9$

Explanation in words

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

cube root in to exponent form as $\frac{1}{3}$

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

Step-by-step explanation:

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

$(b^{27})^{\frac{1}{3}}$

Because, by definition $\sqrt[n]{x}=x^{\frac{1}{n}}$

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

$b^{\frac{27}{3}}$

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

 $b^{9}$