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Without using the exponent law (x^a)^b = x^ab, show that (8^-2)^3 = 1/8^6.

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It is required to prove:


(8^(-2))^3=(1)/(8^6)

To prove without using the exponent law (x^a)^b = x^ab

So, find the value of each side

so,

The left side =


(8^(-2))^3=((1)/(8^2))^3=((1)/(64))^3=(1^3)/(64^3)=(1)/(64\cdot64\cdot64)=(1)/(262,144)

The right side =


(1)/(8^6)=(1)/(8\cdot8\cdot8\cdot8\cdot8\cdot8)=(1)/(262,144)

so, the left side = the right side

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