Solve frac{(-8x^{3}y^{2})^{2}*2x^2y^6}{32x^6y^3}

$$\frac { ( - 8 x ^ { 3 } y ^ { 2 } ) ^ { 2 } \cdot 2 x ^ { 2 } y ^ { 6 } } { 32 x ^ { 6 } y ^ { 3 } }$$

Evaluate

$$4x^{2}y^{7}$$

Solution Steps

Cancel out 2x^{2}y^{3} in both numerator and denominator.

$$\frac{y^{3}\left(-8y^{2}x^{3}\right)^{2}}{16x^{4}}$$

Expand \left(-8y^{2}x^{3}\right)^{2}.

$$\frac{y^{3}\left(-8\right)^{2}\left(y^{2}\right)^{2}\left(x^{3}\right)^{2}}{16x^{4}}$$

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

$$\frac{y^{3}\left(-8\right)^{2}y^{4}\left(x^{3}\right)^{2}}{16x^{4}}$$

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

$$\frac{y^{3}\left(-8\right)^{2}y^{4}x^{6}}{16x^{4}}$$

Calculate -8 to the power of 2 and get 64.

$$\frac{y^{3}\times 64y^{4}x^{6}}{16x^{4}}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{y^{7}\times 64x^{6}}{16x^{4}}$$

Cancel out 16x^{4} in both numerator and denominator.

$$4x^{2}y^{7}$$

Expand

$$4x^{2}y^{7}$$

Solution Steps

Cancel out 2x^{2}y^{3} in both numerator and denominator.

$$\frac{y^{3}\left(-8y^{2}x^{3}\right)^{2}}{16x^{4}}$$

Expand \left(-8y^{2}x^{3}\right)^{2}.

$$\frac{y^{3}\left(-8\right)^{2}\left(y^{2}\right)^{2}\left(x^{3}\right)^{2}}{16x^{4}}$$

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

$$\frac{y^{3}\left(-8\right)^{2}y^{4}\left(x^{3}\right)^{2}}{16x^{4}}$$

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

$$\frac{y^{3}\left(-8\right)^{2}y^{4}x^{6}}{16x^{4}}$$

Calculate -8 to the power of 2 and get 64.

$$\frac{y^{3}\times 64y^{4}x^{6}}{16x^{4}}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{y^{7}\times 64x^{6}}{16x^{4}}$$

Cancel out 16x^{4} in both numerator and denominator.

$$4x^{2}y^{7}$$