Solve (4x^-4y^3)^-2

$$( 4 x ^ { - 4 } y ^ { 3 } ) ^ { - 2 }$$

Evaluate

$$\frac{x^{8}}{16y^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4x^{-4}y^{3}\right)^{-2}$$

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

$$4^{-2}\left(x^{-4}\right)^{-2}\left(y^{3}\right)^{-2}$$

Raise 4 to the power -2.

$$\frac{1}{16}\left(x^{-4}\right)^{-2}\left(y^{3}\right)^{-2}$$

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

$$\frac{1}{16}x^{-4\left(-2\right)}y^{3\left(-2\right)}$$

Multiply -4 times -2.

$$\frac{1}{16}x^{8}y^{3\left(-2\right)}$$

Multiply 3 times -2.

$$\frac{1}{16}x^{8}\times \frac{1}{y^{6}}$$

Expand

$$\frac{x^{8}}{16y^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4x^{-4}y^{3}\right)^{-2}$$

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

$$4^{-2}\left(x^{-4}\right)^{-2}\left(y^{3}\right)^{-2}$$

Raise 4 to the power -2.

$$\frac{1}{16}\left(x^{-4}\right)^{-2}\left(y^{3}\right)^{-2}$$

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

$$\frac{1}{16}x^{-4\left(-2\right)}y^{3\left(-2\right)}$$

Multiply -4 times -2.

$$\frac{1}{16}x^{8}y^{3\left(-2\right)}$$

Multiply 3 times -2.

$$\frac{1}{16}x^{8}\times \frac{1}{y^{6}}$$