To determine if \( 5 \) is equal to \( 5^3 \times 5^{-5} \), we can use the laws of exponents.
According to the laws of exponents, when multiplying numbers with the same base, we add the exponents:
\[ 5^3 \times 5^{-5} = 5^{3 + (-5)} = 5^{3 - 5} = 5^{-2} \]
Now we can simplify \( 5^{-2} \):
\[ 5^{-2} = \frac{1}{5^2} = \frac{1}{25} \]
So, we find that:
\[ 5^3 \times 5^{-5} = \frac{1}{25} \]
Thus, \( 5 \) is not equal to \( 5^3 \times 5^{-5} \); in fact, \( 5^3 \times 5^{-5} = \frac{1}{25} \).
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