Please show how to solve this with step by step. (4a^2b^–2)^3

We are asked to simplify the expression . (Note that we cannot be asked to solve since this is not an equation; there is no equals sign (or inequality, etc...))

We will use the exponent rules. There are a number of different approaches.

(1) First use the product to a power rule: This is something like a distributive property of exponents over multiplication instead of multiplication over addition.

** The equals sign here does not create an equation to solve; it indicates an identity or that both sides are equivalent expressions.

(2) Now we will use the power to a power rule: This rule comes from the definition of exponents (at least for integral exponents):

So

(3) Finally we use the negative exponent rule:

This is often given as , but we can combine this rule with the power to a power rule. Thus

So we have

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The expression simplifies to the equivalent expression

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