High School

We appreciate your visit to Simplify tex left k 4 right frac 3 2 tex A tex 3125 k 5 tex B tex 16 k 8 tex C tex 32. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Simplify \([tex]\left(k^4\right)^{\frac{3}{2}}[/tex]\).

A) \([tex]3125 k^5[/tex]\)

B) \([tex]16 k^8[/tex]\)

C) \([tex]32 k^5[/tex]\)

D) \([tex]k^6[/tex]\)

Answer :

To solve the expression [tex]\((k^4)^{\frac{3}{2}}\)[/tex], we can use the rule for powers of powers, which states that [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]. Here's a step-by-step breakdown:

1. Identify the Expression: We start with [tex]\((k^4)^{\frac{3}{2}}\)[/tex].

2. Apply the Power of a Power Rule: According to the rule, we multiply the exponents. So, [tex]\((k^4)^{\frac{3}{2}} = k^{4 \cdot \frac{3}{2}}\)[/tex].

3. Calculate the New Exponent:
- Multiply the exponents: [tex]\(4 \times \frac{3}{2} = 6\)[/tex].

4. Simplify the Expression: The expression simplifies to [tex]\(k^6\)[/tex].

Thus, the final answer is [tex]\(k^6\)[/tex], which corresponds to option D.

Thanks for taking the time to read Simplify tex left k 4 right frac 3 2 tex A tex 3125 k 5 tex B tex 16 k 8 tex C tex 32. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

Other Questions