Question
Four to the eighth power times four to the power equals one
Answers
GPT-4o mini
To solve the equation \( 4^8 \times 4^x = 1 \), we start by using the property of exponents that states when multiplying the same base, we can add the exponents:
\[
4^8 \times 4^x = 4^{8+x}
\]
We want to set this equal to 1:
\[
4^{8+x} = 1
\]
We know that any non-zero base raised to the power of 0 equals 1:
\[
4^0 = 1
\]
Therefore, for \( 4^{8+x} \) to equal 1, we need:
\[
8 + x = 0
\]
Now, we solve for \( x \):
\[
x = -8
\]
Thus, the solution to the equation \( 4^8 \times 4^x = 1 \) is:
\[
\boxed{-8}
\]
\[
4^8 \times 4^x = 4^{8+x}
\]
We want to set this equal to 1:
\[
4^{8+x} = 1
\]
We know that any non-zero base raised to the power of 0 equals 1:
\[
4^0 = 1
\]
Therefore, for \( 4^{8+x} \) to equal 1, we need:
\[
8 + x = 0
\]
Now, we solve for \( x \):
\[
x = -8
\]
Thus, the solution to the equation \( 4^8 \times 4^x = 1 \) is:
\[
\boxed{-8}
\]