Question

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1 fill in the blank 1 point
in the equation $(k^{\frac{3}{4}})(k^{\frac{1}{4}})^{5}=k^{x}$, what is the value of x that makes the equation true?
$x=$ type your answer...

Explanation:

Step1: Simplify the exponent term

First, apply the power of a power rule: $(a^m)^n=a^{m \times n}$. For $(k^{\frac{1}{4}})^5$, calculate the exponent:
$\frac{1}{4} \times 5 = \frac{5}{4}$
So the term becomes $k^{\frac{5}{4}}$.

Step2: Combine the like terms

Use the product rule for exponents: $a^m \times a^n = a^{m+n}$. Add the exponents of $k$:
$\frac{3}{4} + \frac{5}{4} = \frac{3+5}{4} = \frac{8}{4}$

Step3: Simplify the resulting fraction

Reduce the fraction to get the final exponent:
$\frac{8}{4} = 2$

Answer:

$2$