Solve 16x^4/y^9div2x^4y^9/7

$$\frac { 16 x ^ { 4 } } { y ^ { 9 } } \div \frac { 2 x ^ { 4 } y ^ { 9 } } { 7 }$$

Evaluate

$$\frac{56}{y^{18}}$$

Solution Steps

Divide \frac{16x^{4}}{y^{9}} by \frac{2x^{4}y^{9}}{7} by multiplying \frac{16x^{4}}{y^{9}} by the reciprocal of \frac{2x^{4}y^{9}}{7}.

$$\frac{16x^{4}\times 7}{y^{9}\times 2x^{4}y^{9}}$$

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

$$\frac{7\times 8}{y^{9}y^{9}}$$

Multiply 7 and 8 to get 56.

$$\frac{56}{y^{9}y^{9}}$$

To multiply powers of the same base, add their exponents. Add 9 and 9 to get 18.

$$\frac{56}{y^{18}}$$

Differentiate w.r.t. y

$$-\frac{1008}{y^{19}}$$