Solve (3xy^6)^2(y^3)^3

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

Evaluate

$$9x^{2}y^{21}$$

Solution Steps

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

$$\left(3xy^{6}\right)^{2}y^{9}$$

Expand \left(3xy^{6}\right)^{2}.

$$3^{2}x^{2}\left(y^{6}\right)^{2}y^{9}$$

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

$$3^{2}x^{2}y^{12}y^{9}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}y^{12}y^{9}$$

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

$$9x^{2}y^{21}$$

Expand

$$9x^{2}y^{21}$$

Solution Steps

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

$$\left(3xy^{6}\right)^{2}y^{9}$$

Expand \left(3xy^{6}\right)^{2}.

$$3^{2}x^{2}\left(y^{6}\right)^{2}y^{9}$$

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

$$3^{2}x^{2}y^{12}y^{9}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}y^{12}y^{9}$$

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

$$9x^{2}y^{21}$$