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.
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.
