Verified Answer :

ayah1

whenever you multiply two numbers with exponents that are the same, ADD the exponents together:

\(5^{2} * 5^{-6} = 5^{2+(-6)} = 5^{-4}\)

when the exponent is a negative just put 1 over the number and lose the negative.... '-'

\(5^{-4} = \frac{1}{5^{4} } = \frac{1}{5*5*5*5*5} = \frac{1}{25*25} = \frac{1}{625}\) or 0.0016

Answer:

1/625

Step-by-step explanation:

Given expression:

\(5^{2} \times 5^{-6\)

\(\boxed{\text{Applying exponent rule}: \huge\text{[} c^{a} \times c^{-r} = c^{a - r} \huge\text{]}}\)

     \(\implies 5^{2} \times 5^{-6\)

     \(\implies 5^{2 - 6}\)

     \(\implies 5^{-4}\)

\(\boxed{\text{Applying exponent rule}: \huge\text{[}r^{-a} = \dfrac{1}{r^{a} }\huge\text{]}}\)

     \(\implies \dfrac{1}{5^{4}} = \dfrac{1}{25^{2}} = \boxed{\dfrac{1}{625}}\)

Therefore, \(5^{2} \times 5^{-6\) is equivalent to 1/625.

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