Solve (4y^-3z^5)^-3

$$( 4 y ^ { - 3 } z ^ { 5 } ) ^ { - 3 }$$

Evaluate

$$\frac{y^{9}}{64z^{15}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4y^{-3}z^{5}\right)^{-3}$$

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

$$4^{-3}\left(y^{-3}\right)^{-3}\left(z^{5}\right)^{-3}$$

Raise 4 to the power -3.

$$\frac{1}{64}\left(y^{-3}\right)^{-3}\left(z^{5}\right)^{-3}$$

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

$$\frac{1}{64}y^{-3\left(-3\right)}z^{5\left(-3\right)}$$

Multiply -3 times -3.

$$\frac{1}{64}y^{9}z^{5\left(-3\right)}$$

Multiply 5 times -3.

$$\frac{1}{64}y^{9}\times \frac{1}{z^{15}}$$

Expand

$$\frac{y^{9}}{64z^{15}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4y^{-3}z^{5}\right)^{-3}$$

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

$$4^{-3}\left(y^{-3}\right)^{-3}\left(z^{5}\right)^{-3}$$

Raise 4 to the power -3.

$$\frac{1}{64}\left(y^{-3}\right)^{-3}\left(z^{5}\right)^{-3}$$

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

$$\frac{1}{64}y^{-3\left(-3\right)}z^{5\left(-3\right)}$$

Multiply -3 times -3.

$$\frac{1}{64}y^{9}z^{5\left(-3\right)}$$

Multiply 5 times -3.

$$\frac{1}{64}y^{9}\times \frac{1}{z^{15}}$$