Question
Use the laws of exponents to solve for x in the equation 4^1/4/x =4 3/4 .(1 point)
Answers
Answered by
GPT-4o mini
To solve the equation
\[
\frac{4^{1/4}}{x} = 4^{3/4},
\]
we can start by isolating \(x\). First, rearrange the equation by multiplying both sides by \(x\):
\[
4^{1/4} = 4^{3/4} \cdot x.
\]
Next, divide both sides by \(4^{3/4}\):
\[
x = \frac{4^{1/4}}{4^{3/4}}.
\]
Using the laws of exponents, specifically \(a^m / a^n = a^{m-n}\), we can simplify the right hand side:
\[
x = 4^{1/4 - 3/4} = 4^{-2/4} = 4^{-1/2}.
\]
Next, we can express \(4^{-1/2}\) in a more recognizable format. Since \(4 = 2^2\), we can rewrite it as:
\[
4^{-1/2} = (2^2)^{-1/2} = 2^{-2/2} = 2^{-1} = \frac{1}{2}.
\]
Thus, the solution for \(x\) is:
\[
x = \frac{1}{2}.
\]
\[
\frac{4^{1/4}}{x} = 4^{3/4},
\]
we can start by isolating \(x\). First, rearrange the equation by multiplying both sides by \(x\):
\[
4^{1/4} = 4^{3/4} \cdot x.
\]
Next, divide both sides by \(4^{3/4}\):
\[
x = \frac{4^{1/4}}{4^{3/4}}.
\]
Using the laws of exponents, specifically \(a^m / a^n = a^{m-n}\), we can simplify the right hand side:
\[
x = 4^{1/4 - 3/4} = 4^{-2/4} = 4^{-1/2}.
\]
Next, we can express \(4^{-1/2}\) in a more recognizable format. Since \(4 = 2^2\), we can rewrite it as:
\[
4^{-1/2} = (2^2)^{-1/2} = 2^{-2/2} = 2^{-1} = \frac{1}{2}.
\]
Thus, the solution for \(x\) is:
\[
x = \frac{1}{2}.
\]