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Simplify the expression so there is only one positive power for each base. (5^-2 x 4^-4)^-2


A. 5^4 x 4^8

B. 1/5^4 x 4^8

C. 1/5^4 x 4^6

D. 5^4 x 4^6

Respuesta :

dalendrk
[tex](a\cdot b)^n=a^n\cdot b^n\\(a^n)^m=a^{n\cdot m}\\\\(5^{-2}\cdot4^{-4})^{-2}=(5^{-2})^{-2}\cdot(4^{-4})^{-2}=5^{-2\cdot(-2)}\cdot4^{-4\cdot(-2)}\\\\=\boxed{5^4\cdot4^8}\to\fbox{A.} [/tex]
MrRoyal

The equivalent expression of (5^-2 x 4^-4)^-2 is 5^4x 4^8

How to simplify the expression?

The expression is given as:

(5^-2 x 4^-4)^-2

Apply the law of indices:

(5^-2 x 4^-4)^-2 = 5^(-2* -2) x 4^(-4 *-2)

Evaluate the product

(5^-2 x 4^-4)^-2 = 5^4x 4^8

Hence, the equivalent expression of (5^-2 x 4^-4)^-2 is 5^4x 4^8

Read more about equivalent expressions at:

https://brainly.com/question/2972832

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