Solve (x^{2}y^5)(3x^3y^-2)^6

$$( x ^ { 2 } y ^ { 5 } ) ( 3 x ^ { 3 } y ^ { - 2 } ) ^ { 6 }$$

Evaluate

$$\frac{729x^{20}}{y^{7}}$$

Solution Steps

Expand \left(3x^{3}y^{-2}\right)^{6}.

$$x^{2}y^{5}\times 3^{6}\left(x^{3}\right)^{6}\left(y^{-2}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$x^{2}y^{5}\times 3^{6}x^{18}\left(y^{-2}\right)^{6}$$

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

$$x^{2}y^{5}\times 3^{6}x^{18}y^{-12}$$

Calculate 3 to the power of 6 and get 729.

$$x^{2}y^{5}\times 729x^{18}y^{-12}$$

To multiply powers of the same base, add their exponents. Add 2 and 18 to get 20.

$$x^{20}y^{5}\times 729y^{-12}$$

To multiply powers of the same base, add their exponents. Add 5 and -12 to get -7.

$$x^{20}y^{-7}\times 729$$

Expand

$$\frac{729x^{20}}{y^{7}}$$

Solution Steps

Expand \left(3x^{3}y^{-2}\right)^{6}.

$$x^{2}y^{5}\times 3^{6}\left(x^{3}\right)^{6}\left(y^{-2}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$x^{2}y^{5}\times 3^{6}x^{18}\left(y^{-2}\right)^{6}$$

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

$$x^{2}y^{5}\times 3^{6}x^{18}y^{-12}$$

Calculate 3 to the power of 6 and get 729.

$$x^{2}y^{5}\times 729x^{18}y^{-12}$$

To multiply powers of the same base, add their exponents. Add 2 and 18 to get 20.

$$x^{20}y^{5}\times 729y^{-12}$$

To multiply powers of the same base, add their exponents. Add 5 and -12 to get -7.

$$x^{20}y^{-7}\times 729$$