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Exercise

$\frac{\left(2a^3\right)^{-2}}{-3a^{-2}}$

Step-by-step Solution

1

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\frac{1}{-3a^{-2}\left(2a^3\right)^{2}}$
2

The power of a product is equal to the product of it's factors raised to the same power

$\frac{1}{-3\cdot 4a^{-2}a^{6}}$
3

Multiply $-3$ times $4$

$\frac{1}{-12a^{-2}a^{6}}$
4

When multiplying exponents with same base we can add the exponents

$\frac{1}{-12a^{4}}$

Final answer to the exercise

$\frac{1}{-12a^{4}}$

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Main Topic: Quotient of Powers

The quotient of powers of same base is equivalent to the same base to the power of the difference of exponents: $\frac{a^m}{a^n}=a^{m-n}$.

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