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

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

Evaluate

$$\frac{64y^{15}}{x^{12}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 3.

$$64\left(x^{-4}\right)^{3}\left(y^{5}\right)^{3}$$

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

$$64x^{-4\times 3}y^{5\times 3}$$

Multiply -4 times 3.

$$64\times \frac{1}{x^{12}}y^{5\times 3}$$

Multiply 5 times 3.

$$64\times \frac{1}{x^{12}}y^{15}$$

Expand

$$\frac{64y^{15}}{x^{12}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 3.

$$64\left(x^{-4}\right)^{3}\left(y^{5}\right)^{3}$$

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

$$64x^{-4\times 3}y^{5\times 3}$$

Multiply -4 times 3.

$$64\times \frac{1}{x^{12}}y^{5\times 3}$$

Multiply 5 times 3.

$$64\times \frac{1}{x^{12}}y^{15}$$