Solve {left(1/3xy^2right)}^2*6x^2y^5=

$${ \left( \frac{ 1 }{ 3 } x { y }^{ 2 } \right) }^{ 2 } \times 6 { x }^{ 2 } { y }^{ 5 } =$$

Evaluate

$$\frac{2x^{4}y^{9}}{3}$$

Solution Steps

Expand \left(\frac{1}{3}xy^{2}\right)^{2}.

$$\left(\frac{1}{3}\right)^{2}x^{2}\left(y^{2}\right)^{2}\times 6x^{2}y^{5}$$

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

$$\left(\frac{1}{3}\right)^{2}x^{2}y^{4}\times 6x^{2}y^{5}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{9}x^{2}y^{4}\times 6x^{2}y^{5}$$

Multiply \frac{1}{9} and 6 to get \frac{2}{3}.

$$\frac{2}{3}x^{2}y^{4}x^{2}y^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{2}{3}x^{4}y^{4}y^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{2}{3}x^{4}y^{9}$$

Expand

$$\frac{2x^{4}y^{9}}{3}$$

Solution Steps

Expand \left(\frac{1}{3}xy^{2}\right)^{2}.

$$\left(\frac{1}{3}\right)^{2}x^{2}\left(y^{2}\right)^{2}\times 6x^{2}y^{5}$$

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

$$\left(\frac{1}{3}\right)^{2}x^{2}y^{4}\times 6x^{2}y^{5}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{9}x^{2}y^{4}\times 6x^{2}y^{5}$$

Multiply \frac{1}{9} and 6 to get \frac{2}{3}.

$$\frac{2}{3}x^{2}y^{4}x^{2}y^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{2}{3}x^{4}y^{4}y^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{2}{3}x^{4}y^{9}$$