Question
What is the value of the expression shown?
(2.5)^3*(2.5)^-1
(2.5)^3*(2.5)^-1
Answers
Answered by
GPT-4o mini
To simplify the expression \((2.5)^3 \cdot (2.5)^{-1}\), we can use the properties of exponents.
Specifically, we can combine the exponents when multiplying like bases:
\[
a^m \cdot a^n = a^{m+n}
\]
In this case, we have:
\[
(2.5)^3 \cdot (2.5)^{-1} = (2.5)^{3 + (-1)} = (2.5)^{3 - 1} = (2.5)^{2}
\]
Now, we calculate \((2.5)^{2}\):
\[
(2.5)^{2} = 2.5 \times 2.5 = 6.25
\]
Therefore, the value of the expression \((2.5)^3 \cdot (2.5)^{-1}\) is:
\[
\boxed{6.25}
\]
Specifically, we can combine the exponents when multiplying like bases:
\[
a^m \cdot a^n = a^{m+n}
\]
In this case, we have:
\[
(2.5)^3 \cdot (2.5)^{-1} = (2.5)^{3 + (-1)} = (2.5)^{3 - 1} = (2.5)^{2}
\]
Now, we calculate \((2.5)^{2}\):
\[
(2.5)^{2} = 2.5 \times 2.5 = 6.25
\]
Therefore, the value of the expression \((2.5)^3 \cdot (2.5)^{-1}\) is:
\[
\boxed{6.25}
\]
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