Solve (3xy^2z^3)^4(y^2z)

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

Evaluate

$$81x^{4}y^{10}z^{13}$$

Solution Steps

Expand \left(3xy^{2}z^{3}\right)^{4}.

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

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

$$3^{4}x^{4}y^{8}\left(z^{3}\right)^{4}y^{2}z$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$3^{4}x^{4}y^{8}z^{12}y^{2}z$$

Calculate 3 to the power of 4 and get 81.

$$81x^{4}y^{8}z^{12}y^{2}z$$

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

$$81x^{4}y^{10}z^{12}z$$

To multiply powers of the same base, add their exponents. Add 12 and 1 to get 13.

$$81x^{4}y^{10}z^{13}$$

Expand

$$81x^{4}y^{10}z^{13}$$

Solution Steps

Expand \left(3xy^{2}z^{3}\right)^{4}.

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

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

$$3^{4}x^{4}y^{8}\left(z^{3}\right)^{4}y^{2}z$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$3^{4}x^{4}y^{8}z^{12}y^{2}z$$

Calculate 3 to the power of 4 and get 81.

$$81x^{4}y^{8}z^{12}y^{2}z$$

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

$$81x^{4}y^{10}z^{12}z$$

To multiply powers of the same base, add their exponents. Add 12 and 1 to get 13.

$$81x^{4}y^{10}z^{13}$$