Solve (4u^4w^3)^3

$$( 4 u ^ { 4 } w ^ { 3 } ) ^ { 3 }$$

Evaluate

$$64w^{9}u^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 3.

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

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

$$64u^{4\times 3}w^{3\times 3}$$

Multiply 4 times 3.

$$64u^{12}w^{3\times 3}$$

Multiply 3 times 3.

$$64u^{12}w^{9}$$

Expand

$$64w^{9}u^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 3.

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

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

$$64u^{4\times 3}w^{3\times 3}$$

Multiply 4 times 3.

$$64u^{12}w^{3\times 3}$$

Multiply 3 times 3.

$$64u^{12}w^{9}$$