Answer: b. b^9
Step-by-step explanation:
1. You can rewrite [tex]\sqrt[3]{b^{27}}[/tex] as following:
[tex](b^{27})^{\frac{1}{3}}[/tex]
Because, by definition [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]
2. Now, keeping on mind the exponents properties, you can multiply the exponents, then you obtain:
[tex]b^{\frac{27}{3}}[/tex]
3. Finally, you must simplify the exponent, then, you obtain the following result:
[tex]b^{9}[/tex]
Answer:
Option b is correct.
Step-by-step explanation:
[tex]\sqrt[3]{b^{27} }) =(b^{27}) ^{\frac{1}{3} } =b^(\frac{27}{3} )= b^9\\[/tex]
Explanation in words
We can write any radical form in to exponent form therefore we wrote
cube root in to exponent form as [tex]\frac{1}{3}[/tex]
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 [tex]b^9[/tex] which gives option b as the answer.
