Solve (2m^2)^-3(-m^-2)^-2

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

Evaluate

$$\frac{1}{8m^{2}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Multiply 2 times -3.

$$2^{-3}m^{-6}m^{-2\left(-2\right)}$$

Multiply -2 times -2.

$$2^{-3}m^{-6}m^{4}$$

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

$$2^{-3}m^{-6+4}$$

Add the exponents -6 and 4.

$$2^{-3}m^{-2}$$

Raise 2 to the power -3.

$$\frac{1}{8}m^{-2}$$

Expand

$$\frac{1}{8m^{2}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Multiply 2 times -3.

$$2^{-3}m^{-6}m^{-2\left(-2\right)}$$

Multiply -2 times -2.

$$2^{-3}m^{-6}m^{4}$$

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

$$2^{-3}m^{-6+4}$$

Add the exponents -6 and 4.

$$2^{-3}m^{-2}$$

Raise 2 to the power -3.

$$\frac{1}{8}m^{-2}$$