Solve (3x^{12}y^{3})^3(4xy^6z^5)^2

$$( 3 x ^ { 12 } y ^ { 3 } ) ^ { 3 } ( 4 x y ^ { 6 } z ^ { 5 } ) ^ { 2 }$$

Evaluate

$$432z^{10}y^{21}x^{38}$$

Solution Steps

Expand \left(3x^{12}y^{3}\right)^{3}.

$$3^{3}\left(x^{12}\right)^{3}\left(y^{3}\right)^{3}\times \left(4xy^{6}z^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 3 to get 36.

$$3^{3}x^{36}\left(y^{3}\right)^{3}\times \left(4xy^{6}z^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$3^{3}x^{36}y^{9}\times \left(4xy^{6}z^{5}\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$27x^{36}y^{9}\times \left(4xy^{6}z^{5}\right)^{2}$$

Expand \left(4xy^{6}z^{5}\right)^{2}.

$$27x^{36}y^{9}\times 4^{2}x^{2}\left(y^{6}\right)^{2}\left(z^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$27x^{36}y^{9}\times 4^{2}x^{2}y^{12}\left(z^{5}\right)^{2}$$

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

$$27x^{36}y^{9}\times 4^{2}x^{2}y^{12}z^{10}$$

Calculate 4 to the power of 2 and get 16.

$$27x^{36}y^{9}\times 16x^{2}y^{12}z^{10}$$

Multiply 27 and 16 to get 432.

$$432x^{36}y^{9}x^{2}y^{12}z^{10}$$

To multiply powers of the same base, add their exponents. Add 36 and 2 to get 38.

$$432x^{38}y^{9}y^{12}z^{10}$$

To multiply powers of the same base, add their exponents. Add 9 and 12 to get 21.

$$432x^{38}y^{21}z^{10}$$

Expand

$$432z^{10}y^{21}x^{38}$$

Solution Steps

Expand \left(3x^{12}y^{3}\right)^{3}.

$$3^{3}\left(x^{12}\right)^{3}\left(y^{3}\right)^{3}\times \left(4xy^{6}z^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 3 to get 36.

$$3^{3}x^{36}\left(y^{3}\right)^{3}\times \left(4xy^{6}z^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$3^{3}x^{36}y^{9}\times \left(4xy^{6}z^{5}\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$27x^{36}y^{9}\times \left(4xy^{6}z^{5}\right)^{2}$$

Expand \left(4xy^{6}z^{5}\right)^{2}.

$$27x^{36}y^{9}\times 4^{2}x^{2}\left(y^{6}\right)^{2}\left(z^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$27x^{36}y^{9}\times 4^{2}x^{2}y^{12}\left(z^{5}\right)^{2}$$

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

$$27x^{36}y^{9}\times 4^{2}x^{2}y^{12}z^{10}$$

Calculate 4 to the power of 2 and get 16.

$$27x^{36}y^{9}\times 16x^{2}y^{12}z^{10}$$

Multiply 27 and 16 to get 432.

$$432x^{36}y^{9}x^{2}y^{12}z^{10}$$

To multiply powers of the same base, add their exponents. Add 36 and 2 to get 38.

$$432x^{38}y^{9}y^{12}z^{10}$$

To multiply powers of the same base, add their exponents. Add 9 and 12 to get 21.

$$432x^{38}y^{21}z^{10}$$