Respuesta :

ayah1
whenever you multiply two numbers with exponents that are the same, ADD the exponents together:

[tex] 5^{2} * 5^{-6} = 5^{2+(-6)} = 5^{-4} [/tex]

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

[tex] 5^{-4} = \frac{1}{5^{4} } = \frac{1}{5*5*5*5*5} = \frac{1}{25*25} = \frac{1}{625} [/tex] or 0.0016

Answer:

1/625

Step-by-step explanation:

Given expression:

[tex]5^{2} \times 5^{-6[/tex]

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

     [tex]\implies 5^{2} \times 5^{-6[/tex]

     [tex]\implies 5^{2 - 6}[/tex]

     [tex]\implies 5^{-4}[/tex]

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

     [tex]\implies \dfrac{1}{5^{4}} = \dfrac{1}{25^{2}} = \boxed{\dfrac{1}{625}}[/tex]

Therefore, [tex]5^{2} \times 5^{-6[/tex] is equivalent to 1/625.

Learn more about exponents: https://brainly.com/question/27748898

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