Solve (4x^2y^-1)^3

$$( 4 x ^ { 2 } y ^ { - 1 } ) ^ { 3 }$$

Evaluate

$$\frac{64x^{6}}{y^{3}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4x^{2}\times \frac{1}{y}\right)^{3}$$

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

$$4^{3}\left(x^{2}\right)^{3}\times \left(\frac{1}{y}\right)^{3}$$

Raise 4 to the power 3.

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

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

$$64x^{2\times 3}y^{-3}$$

Multiply 2 times 3.

$$64x^{6}y^{-3}$$

Multiply -1 times 3.

$$64x^{6}\times \frac{1}{y^{3}}$$

Expand

$$\frac{64x^{6}}{y^{3}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4x^{2}\times \frac{1}{y}\right)^{3}$$

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

$$4^{3}\left(x^{2}\right)^{3}\times \left(\frac{1}{y}\right)^{3}$$

Raise 4 to the power 3.

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

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

$$64x^{2\times 3}y^{-3}$$

Multiply 2 times 3.

$$64x^{6}y^{-3}$$

Multiply -1 times 3.

$$64x^{6}\times \frac{1}{y^{3}}$$