Solve (5vw^2)^3

$$( 5 v w ^ { 2 } ) ^ { 3 }$$

Evaluate

$$125v^{3}w^{6}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5v^{1}w^{2}\right)^{3}$$

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

$$5^{3}\left(v^{1}\right)^{3}\left(w^{2}\right)^{3}$$

Raise 5 to the power 3.

$$125\left(v^{1}\right)^{3}\left(w^{2}\right)^{3}$$

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

$$125v^{3}w^{2\times 3}$$

Multiply 2 times 3.

$$125v^{3}w^{6}$$

Expand

$$125v^{3}w^{6}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5v^{1}w^{2}\right)^{3}$$

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

$$5^{3}\left(v^{1}\right)^{3}\left(w^{2}\right)^{3}$$

Raise 5 to the power 3.

$$125\left(v^{1}\right)^{3}\left(w^{2}\right)^{3}$$

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

$$125v^{3}w^{2\times 3}$$

Multiply 2 times 3.

$$125v^{3}w^{6}$$