IDNLearn.com offers a unique blend of expert answers and community-driven knowledge. Ask your questions and receive accurate, in-depth answers from our knowledgeable community members.

Given that the cube root of 27 is 3, what is [tex]$27^{\frac{4}{3}}$[/tex]?

A. 108
B. 81
C. 4
D. 12


Sagot :

Sure, let's solve the problem step-by-step.

First, we need to understand what [tex]\( 27^{\frac{4}{3}} \)[/tex] represents. This expression involves taking the base number 27 to the power of [tex]\( \frac{4}{3} \)[/tex].

1. Understanding the Exponent: The exponent [tex]\( \frac{4}{3} \)[/tex] can be broken down into two parts:
- The denominator (3) signifies that we take the cube root of 27.
- The numerator (4) indicates that we then raise that result to the power of 4.

2. Step by Step Calculation:
- Step 1: Compute the Cube Root:
[tex]\(\sqrt[3]{27} = 3\)[/tex]
(Since the cube root of 27 is 3)

- Step 2: Raise to the Power of 4:
[tex]\((3)^4 = 81\)[/tex]

So, [tex]\( 27^{\frac{4}{3}} = 81 \)[/tex].

Therefore, the correct answer is [tex]\( 81 \)[/tex].
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.