Question
An expression is shown.
`2^{3}\cdot2^{-5}`
What is the value of the expression?
`2^{3}\cdot2^{-5}`
What is the value of the expression?
Answers
GPT-4o mini
To simplify the expression \( 2^{3} \cdot 2^{-5} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
Applying this property:
\[
2^{3} \cdot 2^{-5} = 2^{3 + (-5)} = 2^{-2}
\]
Now, to find \( 2^{-2} \), you can rewrite it as:
\[
2^{-2} = \frac{1}{2^{2}} = \frac{1}{4}
\]
Thus, the value of the expression \( 2^{3} \cdot 2^{-5} \) is
\[
\frac{1}{4}
\]
Applying this property:
\[
2^{3} \cdot 2^{-5} = 2^{3 + (-5)} = 2^{-2}
\]
Now, to find \( 2^{-2} \), you can rewrite it as:
\[
2^{-2} = \frac{1}{2^{2}} = \frac{1}{4}
\]
Thus, the value of the expression \( 2^{3} \cdot 2^{-5} \) is
\[
\frac{1}{4}
\]