Solve [(2x^2y^3)^2/3x^-2y]

$$[ \frac { ( 2 x ^ { 2 } y ^ { 3 } ) ^ { 2 } } { 3 x ^ { - 2 } y } ]$$

Evaluate

$$\frac{4y^{5}x^{6}}{3}$$

Solution Steps

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

$$\frac{2^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}}{3x^{-2}y}$$

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{2^{2}x^{4}y^{6}}{3x^{-2}y}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{4}y^{6}}{3x^{-2}y}$$

Cancel out y in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{4y^{5}x^{6}}{3}$$

Expand

$$\frac{4y^{5}x^{6}}{3}$$

Solution Steps

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

$$\frac{2^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}}{3x^{-2}y}$$

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{2^{2}x^{4}y^{6}}{3x^{-2}y}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{4}y^{6}}{3x^{-2}y}$$

Cancel out y in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{4y^{5}x^{6}}{3}$$