Solve (2xy^{2})^4(3x^3y^2z^3)

$$( 2 x y ^ { 2 } ) ^ { 4 } ( 3 x ^ { 3 } y ^ { 2 } z ^ { 3 } )$$

Evaluate

$$48z^{3}x^{7}y^{10}$$

Solution Steps

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

$$2^{4}x^{4}\left(y^{2}\right)^{4}\times 3x^{3}y^{2}z^{3}$$

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

$$2^{4}x^{4}y^{8}\times 3x^{3}y^{2}z^{3}$$

Calculate 2 to the power of 4 and get 16.

$$16x^{4}y^{8}\times 3x^{3}y^{2}z^{3}$$

Multiply 16 and 3 to get 48.

$$48x^{4}y^{8}x^{3}y^{2}z^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$48x^{7}y^{8}y^{2}z^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$48x^{7}y^{10}z^{3}$$

Expand

$$48z^{3}x^{7}y^{10}$$

Solution Steps

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

$$2^{4}x^{4}\left(y^{2}\right)^{4}\times 3x^{3}y^{2}z^{3}$$

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

$$2^{4}x^{4}y^{8}\times 3x^{3}y^{2}z^{3}$$

Calculate 2 to the power of 4 and get 16.

$$16x^{4}y^{8}\times 3x^{3}y^{2}z^{3}$$

Multiply 16 and 3 to get 48.

$$48x^{4}y^{8}x^{3}y^{2}z^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$48x^{7}y^{8}y^{2}z^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$48x^{7}y^{10}z^{3}$$