Solve (4x^8y^-2)^-3

$$( 4 x ^ { 8 } y ^ { - 2 } ) ^ { - 3 }$$

Evaluate

$$\frac{y^{6}}{64x^{24}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4x^{8}y^{-2}\right)^{-3}$$

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

$$4^{-3}\left(x^{8}\right)^{-3}\left(y^{-2}\right)^{-3}$$

Raise 4 to the power -3.

$$\frac{1}{64}\left(x^{8}\right)^{-3}\left(y^{-2}\right)^{-3}$$

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

$$\frac{1}{64}x^{8\left(-3\right)}y^{-2\left(-3\right)}$$

Multiply 8 times -3.

$$\frac{1}{64}\times \frac{1}{x^{24}}y^{-2\left(-3\right)}$$

Multiply -2 times -3.

$$\frac{1}{64}\times \frac{1}{x^{24}}y^{6}$$

Expand

$$\frac{y^{6}}{64x^{24}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4x^{8}y^{-2}\right)^{-3}$$

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

$$4^{-3}\left(x^{8}\right)^{-3}\left(y^{-2}\right)^{-3}$$

Raise 4 to the power -3.

$$\frac{1}{64}\left(x^{8}\right)^{-3}\left(y^{-2}\right)^{-3}$$

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

$$\frac{1}{64}x^{8\left(-3\right)}y^{-2\left(-3\right)}$$

Multiply 8 times -3.

$$\frac{1}{64}\times \frac{1}{x^{24}}y^{-2\left(-3\right)}$$

Multiply -2 times -3.

$$\frac{1}{64}\times \frac{1}{x^{24}}y^{6}$$