Solve frac{8xy^{3}*2x^{3}y^{4}}{(-7x^3y)^2-x^6y^2}

$$\frac { 8 x y ^ { 3 } \cdot 2 x ^ { 3 } y ^ { 4 } } { ( - 7 x ^ { 3 } y ) ^ { 2 } - x ^ { 6 } y ^ { 2 } }$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{8x^{4}y^{3}\times 2y^{4}}{\left(-7x^{3}y\right)^{2}-x^{6}y^{2}}$$

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

$$\frac{8x^{4}y^{7}\times 2}{\left(-7x^{3}y\right)^{2}-x^{6}y^{2}}$$

Multiply 8 and 2 to get 16.

$$\frac{16x^{4}y^{7}}{\left(-7x^{3}y\right)^{2}-x^{6}y^{2}}$$

Expand \left(-7x^{3}y\right)^{2}.

$$\frac{16x^{4}y^{7}}{\left(-7\right)^{2}\left(x^{3}\right)^{2}y^{2}-x^{6}y^{2}}$$

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

$$\frac{16x^{4}y^{7}}{\left(-7\right)^{2}x^{6}y^{2}-x^{6}y^{2}}$$

Calculate -7 to the power of 2 and get 49.

$$\frac{16x^{4}y^{7}}{49x^{6}y^{2}-x^{6}y^{2}}$$

Combine 49x^{6}y^{2} and -x^{6}y^{2} to get 48x^{6}y^{2}.

$$\frac{16x^{4}y^{7}}{48x^{6}y^{2}}$$

Cancel out 16y^{2}x^{4} in both numerator and denominator.

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

Expand

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{8x^{4}y^{3}\times 2y^{4}}{\left(-7x^{3}y\right)^{2}-x^{6}y^{2}}$$

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

$$\frac{8x^{4}y^{7}\times 2}{\left(-7x^{3}y\right)^{2}-x^{6}y^{2}}$$

Multiply 8 and 2 to get 16.

$$\frac{16x^{4}y^{7}}{\left(-7x^{3}y\right)^{2}-x^{6}y^{2}}$$

Expand \left(-7x^{3}y\right)^{2}.

$$\frac{16x^{4}y^{7}}{\left(-7\right)^{2}\left(x^{3}\right)^{2}y^{2}-x^{6}y^{2}}$$

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

$$\frac{16x^{4}y^{7}}{\left(-7\right)^{2}x^{6}y^{2}-x^{6}y^{2}}$$

Calculate -7 to the power of 2 and get 49.

$$\frac{16x^{4}y^{7}}{49x^{6}y^{2}-x^{6}y^{2}}$$

Combine 49x^{6}y^{2} and -x^{6}y^{2} to get 48x^{6}y^{2}.

$$\frac{16x^{4}y^{7}}{48x^{6}y^{2}}$$

Cancel out 16y^{2}x^{4} in both numerator and denominator.

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