Solve frac{8(-2x^{3}y^2)^2}{2x^-3y^-2}

$$\frac { 8 ( - 2 x ^ { 3 } y ^ { 2 } ) ^ { 2 } } { 2 x ^ { - 3 } y ^ { - 2 } }$$

Evaluate

$$16y^{6}x^{9}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

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

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

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

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

Calculate -2 to the power of 2 and get 4.

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

Multiply 4 and 4 to get 16.

$$\frac{16y^{4}x^{6}}{x^{-3}y^{-2}}$$

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

$$16y^{6}x^{9}$$

Expand

$$16y^{6}x^{9}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

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

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

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

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

Calculate -2 to the power of 2 and get 4.

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

Multiply 4 and 4 to get 16.

$$\frac{16y^{4}x^{6}}{x^{-3}y^{-2}}$$

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

$$16y^{6}x^{9}$$