How do you evaluate the expression #(5^-2)^2# using the properties?

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Answer 1 · 2017-06-20T14:21:57

See a solution process below:

First, use this property of exponents to eliminate the outer exponent:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#(5^color(red)(-2))^color(blue)(2) = 5^(color(red)(-2) xx color(blue)(2)) = 5^-4#

Now, use this property of exponents to eliminate the negative exponent:

#x^color(red)(a) = 1/x^color(red)(-a)#

#5^color(red)(-4) = 1/5^color(red)(- -4) = 1/5^4#

Now, use the definition of exponents to complete the evaluation:

#1/5^4 = 1/( 5 xx 5 xx 5 xx 5) = 1/(25 xx 25) = 1/625#

Answer 2 · 2017-06-20T14:26:48

Write the expression in an expanded form and adjust the exponents.

# (5^-2)^2 = (5^-2) xx ( 5^-2) #

#(5^-2) xx (5^-2) = 5^-4#

# 5^-4 = 1/5^4#

# 1/5^4 = 1/ (5 xx 5 xx 5 xx 5)#

# 1/( 5 xx 5 xx 5 xx 5) = 1/625#