Question
be to the power of four divided by B to the power of? equals B to the power of 10 what is?
Answers
GPT-4o mini
Let's start with the equation you're trying to solve:
\[
\frac{A^4}{B^x} = B^{10}
\]
To solve for \( x \), we can rearrange the equation. Multiply both sides by \( B^x \) to eliminate the denominator:
\[
A^4 = B^{10} \cdot B^x
\]
Using the property of exponents that states \( B^m \cdot B^n = B^{m+n} \), we can rewrite the right side:
\[
A^4 = B^{10 + x}
\]
For this equation to hold true, the bases must be equal, or we must express one side in terms of the other. Therefore, we can set up the equation for the exponents:
1. If we assume \( A = B \) (just for the sake of this step), we have:
\[
4 = 10 + x
\]
Now, solve for \( x \):
\[
x = 4 - 10
\]
\[
x = -6
\]
Thus, \( x = -6 \) if \( A = B \).
In general, if \( A \) is not explicitly defined in relation to \( B \), then you cannot definitively find a relationship for \( x \) without more information regarding \( A \) or recognizing another condition. However, if the context or intent was different, please provide more details!
\[
\frac{A^4}{B^x} = B^{10}
\]
To solve for \( x \), we can rearrange the equation. Multiply both sides by \( B^x \) to eliminate the denominator:
\[
A^4 = B^{10} \cdot B^x
\]
Using the property of exponents that states \( B^m \cdot B^n = B^{m+n} \), we can rewrite the right side:
\[
A^4 = B^{10 + x}
\]
For this equation to hold true, the bases must be equal, or we must express one side in terms of the other. Therefore, we can set up the equation for the exponents:
1. If we assume \( A = B \) (just for the sake of this step), we have:
\[
4 = 10 + x
\]
Now, solve for \( x \):
\[
x = 4 - 10
\]
\[
x = -6
\]
Thus, \( x = -6 \) if \( A = B \).
In general, if \( A \) is not explicitly defined in relation to \( B \), then you cannot definitively find a relationship for \( x \) without more information regarding \( A \) or recognizing another condition. However, if the context or intent was different, please provide more details!