Solve (a^-3b^2)^-1

$$( a ^ { - 3 } b ^ { 2 } ) ^ { - 1 }$$

Evaluate

$$\frac{a^{3}}{b^{2}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\frac{1}{a^{-3}b^{2}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\frac{1}{a^{-3}}\times \frac{1}{b^{2}}$$

To raise a power to another power, multiply the exponents.

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

Multiply -3 times -1.

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

Multiply 2 times -1.

$$a^{3}\times \frac{1}{b^{2}}$$

Differentiate w.r.t. a

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