# How do you simplify #(3a^-1)^-1 (9a^2 b^3)^-2#?

Start by recognizing that a negative exponent can be written as

Now, notice that you can rewrite the first term of the expression as

In this case, you have

The second term of the expression will be

This means that you have

This can be simplifed to

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To simplify the expression (3a^-1)^-1 (9a^2 b^3)^-2, we first apply the negative exponent rule to rewrite the expressions as fractions. Then, we multiply the fractions together and simplify the result.

(3a^-1)^-1 = (1/(3a^-1))^(-1) = 3a^1

(9a^2 b^3)^-2 = (1/(9a^2 b^3))^(-2) = (9^2 a^(-2*2) b^(-3*2)) = (81/a^4 b^6)

Multiplying the fractions together, we get:

3a^1 * (81/a^4 b^6)

Simplifying the expression further, we combine like terms in the numerator and denominator:

(3 * 81) * (a^1 / a^4) * (1 / b^6) = 243 / (a^3 b^6)

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