Question
Use the laws of exponents to solve for x in the equation 4^1/4/x=4^3/4
.(1 point)
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2
−12
negative Start Fraction 1 over 2 End Fraction
16
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12
Start Fraction 1 over 2 End Fraction
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.(1 point)
Responses
2
2
−12
negative Start Fraction 1 over 2 End Fraction
16
16
12
Start Fraction 1 over 2 End Fraction
Skip to navigation
page 21 of 21
Answers
GPT-4o mini
To solve the equation
\[
\frac{4^{1/4}}{x} = 4^{3/4},
\]
we can start by isolating \( x \).
1. Multiply both sides by \( x \):
\[
4^{1/4} = x \cdot 4^{3/4}.
\]
2. Divide both sides by \( 4^{3/4} \):
\[
x = \frac{4^{1/4}}{4^{3/4}}.
\]
3. Now, we can use the laws of exponents. When you divide two exponents with the same base, you subtract the exponents:
\[
x = 4^{1/4 - 3/4} = 4^{-2/4} = 4^{-1/2}.
\]
4. We can rewrite \( 4^{-1/2} \):
\[
x = \frac{1}{4^{1/2}} = \frac{1}{\sqrt{4}} = \frac{1}{2}.
\]
So, the value of \( x \) is
\[
\frac{1}{2}.
\]
Thus, the answer is
\[
\frac{1}{2}.
\]
\[
\frac{4^{1/4}}{x} = 4^{3/4},
\]
we can start by isolating \( x \).
1. Multiply both sides by \( x \):
\[
4^{1/4} = x \cdot 4^{3/4}.
\]
2. Divide both sides by \( 4^{3/4} \):
\[
x = \frac{4^{1/4}}{4^{3/4}}.
\]
3. Now, we can use the laws of exponents. When you divide two exponents with the same base, you subtract the exponents:
\[
x = 4^{1/4 - 3/4} = 4^{-2/4} = 4^{-1/2}.
\]
4. We can rewrite \( 4^{-1/2} \):
\[
x = \frac{1}{4^{1/2}} = \frac{1}{\sqrt{4}} = \frac{1}{2}.
\]
So, the value of \( x \) is
\[
\frac{1}{2}.
\]
Thus, the answer is
\[
\frac{1}{2}.
\]