Solve (2w^{2}x^3y)^2(x^4y)^5

$$( 2 w ^ { 2 } x ^ { 3 } y ) ^ { 2 } ( x ^ { 4 } y ) ^ { 5 }$$

Evaluate

$$4w^{4}y^{7}x^{26}$$

Solution Steps

Expand \left(2w^{2}x^{3}y\right)^{2}.

$$2^{2}\left(w^{2}\right)^{2}\left(x^{3}\right)^{2}y^{2}\left(x^{4}y\right)^{5}$$

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

$$2^{2}w^{4}\left(x^{3}\right)^{2}y^{2}\left(x^{4}y\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$2^{2}w^{4}x^{6}y^{2}\left(x^{4}y\right)^{5}$$

Calculate 2 to the power of 2 and get 4.

$$4w^{4}x^{6}y^{2}\left(x^{4}y\right)^{5}$$

Expand \left(x^{4}y\right)^{5}.

$$4w^{4}x^{6}y^{2}\left(x^{4}\right)^{5}y^{5}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$4w^{4}x^{6}y^{2}x^{20}y^{5}$$

To multiply powers of the same base, add their exponents. Add 6 and 20 to get 26.

$$4w^{4}x^{26}y^{2}y^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$4w^{4}x^{26}y^{7}$$

Expand

$$4w^{4}y^{7}x^{26}$$

Solution Steps

Expand \left(2w^{2}x^{3}y\right)^{2}.

$$2^{2}\left(w^{2}\right)^{2}\left(x^{3}\right)^{2}y^{2}\left(x^{4}y\right)^{5}$$

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

$$2^{2}w^{4}\left(x^{3}\right)^{2}y^{2}\left(x^{4}y\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$2^{2}w^{4}x^{6}y^{2}\left(x^{4}y\right)^{5}$$

Calculate 2 to the power of 2 and get 4.

$$4w^{4}x^{6}y^{2}\left(x^{4}y\right)^{5}$$

Expand \left(x^{4}y\right)^{5}.

$$4w^{4}x^{6}y^{2}\left(x^{4}\right)^{5}y^{5}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$4w^{4}x^{6}y^{2}x^{20}y^{5}$$

To multiply powers of the same base, add their exponents. Add 6 and 20 to get 26.

$$4w^{4}x^{26}y^{2}y^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$4w^{4}x^{26}y^{7}$$