Question
Use the laws of exponents to solve for x in the equation.
4 1/4 / x = 4 3/4
A. 1/2
B. 2
C. -1/2
D. 16
4 1/4 / x = 4 3/4
A. 1/2
B. 2
C. -1/2
D. 16
Answers
GPT-4o mini
To solve the equation \( \frac{4^{1/4}}{x} = 4^{3/4} \), we can use the properties of exponents.
First, let's express both sides with a common base. We can rewrite the equation as follows:
\[
4^{1/4} = 4^{3/4} \cdot x
\]
Next, we can divide both sides by \(4^{3/4}\):
\[
x = \frac{4^{1/4}}{4^{3/4}}
\]
Using the laws of exponents, particularly \( \frac{a^m}{a^n} = a^{m-n} \), we have:
\[
x = 4^{1/4 - 3/4} = 4^{-2/4} = 4^{-1/2}
\]
Now we can rewrite \(4^{-1/2}\) in radical form:
\[
x = \frac{1}{4^{1/2}} = \frac{1}{\sqrt{4}} = \frac{1}{2}
\]
Thus, the solution for \(x\) is:
\[
\boxed{\frac{1}{2}}
\]
So the answer is **A. 1/2.**
First, let's express both sides with a common base. We can rewrite the equation as follows:
\[
4^{1/4} = 4^{3/4} \cdot x
\]
Next, we can divide both sides by \(4^{3/4}\):
\[
x = \frac{4^{1/4}}{4^{3/4}}
\]
Using the laws of exponents, particularly \( \frac{a^m}{a^n} = a^{m-n} \), we have:
\[
x = 4^{1/4 - 3/4} = 4^{-2/4} = 4^{-1/2}
\]
Now we can rewrite \(4^{-1/2}\) in radical form:
\[
x = \frac{1}{4^{1/2}} = \frac{1}{\sqrt{4}} = \frac{1}{2}
\]
Thus, the solution for \(x\) is:
\[
\boxed{\frac{1}{2}}
\]
So the answer is **A. 1/2.**