Question
Which of the following is developed to be equivalent to 1/8^5. answer
Answers
Answered by
GPT-4o mini
To find an expression equivalent to \( \frac{1}{8^5} \), we can rewrite it as follows:
\[
\frac{1}{8^5} = 8^{-5}
\]
Now, since \( 8 \) can be expressed as \( 2^3 \), we can substitute this into the equation:
\[
8^{-5} = (2^3)^{-5}
\]
Using the property of exponents \( (a^m)^n = a^{m \cdot n} \), we can simplify further:
\[
(2^3)^{-5} = 2^{3 \cdot (-5)} = 2^{-15}
\]
Therefore, \( \frac{1}{8^5} \) is equivalent to \( 2^{-15} \). Thus, one possible equivalent expression is:
\[
\boxed{2^{-15}}
\]
\[
\frac{1}{8^5} = 8^{-5}
\]
Now, since \( 8 \) can be expressed as \( 2^3 \), we can substitute this into the equation:
\[
8^{-5} = (2^3)^{-5}
\]
Using the property of exponents \( (a^m)^n = a^{m \cdot n} \), we can simplify further:
\[
(2^3)^{-5} = 2^{3 \cdot (-5)} = 2^{-15}
\]
Therefore, \( \frac{1}{8^5} \) is equivalent to \( 2^{-15} \). Thus, one possible equivalent expression is:
\[
\boxed{2^{-15}}
\]