Solve (-2h^2)^2(3h^-3)^-2

$$( - 2 h ^ { 2 } ) ^ { 2 } ( 3 h ^ { - 3 } ) ^ { - 2 }$$

Evaluate

$$\frac{4h^{10}}{9}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-2h^{2}\right)^{2}\times \left(3h^{-3}\right)^{-2}$$

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

$$\left(-2\right)^{2}\left(h^{2}\right)^{2}\times 3^{-2}\left(h^{-3}\right)^{-2}$$

Use the Commutative Property of Multiplication.

$$\left(-2\right)^{2}\times 3^{-2}\left(h^{2}\right)^{2}\left(h^{-3}\right)^{-2}$$

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

$$\left(-2\right)^{2}\times 3^{-2}h^{2\times 2}h^{-3\left(-2\right)}$$

Multiply 2 times 2.

$$\left(-2\right)^{2}\times 3^{-2}h^{4}h^{-3\left(-2\right)}$$

Multiply -3 times -2.

$$\left(-2\right)^{2}\times 3^{-2}h^{4}h^{6}$$

To multiply powers of the same base, add their exponents.

$$\left(-2\right)^{2}\times 3^{-2}h^{4+6}$$

Add the exponents 4 and 6.

$$\left(-2\right)^{2}\times 3^{-2}h^{10}$$

Raise -2 to the power 2.

$$4\times 3^{-2}h^{10}$$

Raise 3 to the power -2.

$$4\times \frac{1}{9}h^{10}$$

Multiply 4 times \frac{1}{9}.

$$\frac{4}{9}h^{10}$$

Expand

$$\frac{4h^{10}}{9}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-2h^{2}\right)^{2}\times \left(3h^{-3}\right)^{-2}$$

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

$$\left(-2\right)^{2}\left(h^{2}\right)^{2}\times 3^{-2}\left(h^{-3}\right)^{-2}$$

Use the Commutative Property of Multiplication.

$$\left(-2\right)^{2}\times 3^{-2}\left(h^{2}\right)^{2}\left(h^{-3}\right)^{-2}$$

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

$$\left(-2\right)^{2}\times 3^{-2}h^{2\times 2}h^{-3\left(-2\right)}$$

Multiply 2 times 2.

$$\left(-2\right)^{2}\times 3^{-2}h^{4}h^{-3\left(-2\right)}$$

Multiply -3 times -2.

$$\left(-2\right)^{2}\times 3^{-2}h^{4}h^{6}$$

To multiply powers of the same base, add their exponents.

$$\left(-2\right)^{2}\times 3^{-2}h^{4+6}$$

Add the exponents 4 and 6.

$$\left(-2\right)^{2}\times 3^{-2}h^{10}$$

Raise -2 to the power 2.

$$4\times 3^{-2}h^{10}$$

Raise 3 to the power -2.

$$4\times \frac{1}{9}h^{10}$$

Multiply 4 times \frac{1}{9}.

$$\frac{4}{9}h^{10}$$