Solve (2y^2w)^4(y^2)^5

$$( 2 y ^ { 2 } w ) ^ { 4 } ( y ^ { 2 } ) ^ { 5 }$$

Evaluate

$$16w^{4}y^{18}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\left(2y^{2}w\right)^{4}y^{10}$$

Expand \left(2y^{2}w\right)^{4}.

$$2^{4}\left(y^{2}\right)^{4}w^{4}y^{10}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$2^{4}y^{8}w^{4}y^{10}$$

Calculate 2 to the power of 4 and get 16.

$$16y^{8}w^{4}y^{10}$$

To multiply powers of the same base, add their exponents. Add 8 and 10 to get 18.

$$16y^{18}w^{4}$$

Expand

$$16w^{4}y^{18}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\left(2y^{2}w\right)^{4}y^{10}$$

Expand \left(2y^{2}w\right)^{4}.

$$2^{4}\left(y^{2}\right)^{4}w^{4}y^{10}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$2^{4}y^{8}w^{4}y^{10}$$

Calculate 2 to the power of 4 and get 16.

$$16y^{8}w^{4}y^{10}$$

To multiply powers of the same base, add their exponents. Add 8 and 10 to get 18.

$$16y^{18}w^{4}$$