Solve left(4x^5y^-3right)^-3

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

Evaluate

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power -3.

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

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

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

Multiply 5 times -3.

$$\frac{1}{64}\times \frac{1}{x^{15}}y^{-3\left(-3\right)}$$

Multiply -3 times -3.

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

Expand

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power -3.

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

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

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

Multiply 5 times -3.

$$\frac{1}{64}\times \frac{1}{x^{15}}y^{-3\left(-3\right)}$$

Multiply -3 times -3.

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