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

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

Evaluate

$$64\times \left(\frac{x}{y}\right)^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 3.

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

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

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

Multiply 4 times 3.

$$64x^{12}y^{-4\times 3}$$

Multiply -4 times 3.

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

Expand

$$64\times \left(\frac{x}{y}\right)^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 3.

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

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

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

Multiply 4 times 3.

$$64x^{12}y^{-4\times 3}$$

Multiply -4 times 3.

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