Solve (4w^5y^4)^3

$$( 4 w ^ { 5 } y ^ { 4 } ) ^ { 3 }$$

Evaluate

$$64y^{12}w^{15}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 3.

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

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

$$64w^{5\times 3}y^{4\times 3}$$

Multiply 5 times 3.

$$64w^{15}y^{4\times 3}$$

Multiply 4 times 3.

$$64w^{15}y^{12}$$

Expand

$$64y^{12}w^{15}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 3.

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

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

$$64w^{5\times 3}y^{4\times 3}$$

Multiply 5 times 3.

$$64w^{15}y^{4\times 3}$$

Multiply 4 times 3.

$$64w^{15}y^{12}$$