Solve (3xy^4)^3(2xy^2)^-2

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

Evaluate

$$\frac{27xy^{8}}{4}$$

Solution Steps

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

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

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

$$3^{3}x^{3}y^{12}\times \left(2xy^{2}\right)^{-2}$$

Calculate 3 to the power of 3 and get 27.

$$27x^{3}y^{12}\times \left(2xy^{2}\right)^{-2}$$

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

$$27x^{3}y^{12}\times 2^{-2}x^{-2}\left(y^{2}\right)^{-2}$$

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

$$27x^{3}y^{12}\times 2^{-2}x^{-2}y^{-4}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$27x^{3}y^{12}\times \frac{1}{4}x^{-2}y^{-4}$$

Multiply 27 and \frac{1}{4} to get \frac{27}{4}.

$$\frac{27}{4}x^{3}y^{12}x^{-2}y^{-4}$$

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$\frac{27}{4}x^{1}y^{12}y^{-4}$$

To multiply powers of the same base, add their exponents. Add 12 and -4 to get 8.

$$\frac{27}{4}x^{1}y^{8}$$

Calculate x to the power of 1 and get x.

$$\frac{27}{4}xy^{8}$$

Expand

$$\frac{27xy^{8}}{4}$$

Solution Steps

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

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

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

$$3^{3}x^{3}y^{12}\times \left(2xy^{2}\right)^{-2}$$

Calculate 3 to the power of 3 and get 27.

$$27x^{3}y^{12}\times \left(2xy^{2}\right)^{-2}$$

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

$$27x^{3}y^{12}\times 2^{-2}x^{-2}\left(y^{2}\right)^{-2}$$

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

$$27x^{3}y^{12}\times 2^{-2}x^{-2}y^{-4}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$27x^{3}y^{12}\times \frac{1}{4}x^{-2}y^{-4}$$

Multiply 27 and \frac{1}{4} to get \frac{27}{4}.

$$\frac{27}{4}x^{3}y^{12}x^{-2}y^{-4}$$

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$\frac{27}{4}x^{1}y^{12}y^{-4}$$

To multiply powers of the same base, add their exponents. Add 12 and -4 to get 8.

$$\frac{27}{4}x^{1}y^{8}$$

Calculate x to the power of 1 and get x.

$$\frac{27}{4}xy^{8}$$