Solve -7x^8/9x^2*81x^5/49x

$$\frac { - 7 x ^ { 8 } } { 9 x ^ { 2 } } \cdot \frac { 81 x ^ { 5 } } { 49 x }$$

Evaluate

$$-\frac{9x^{10}}{7}$$

Solution Steps

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

$$\frac{-7x^{6}}{9}\times \frac{81x^{5}}{49x}$$

Cancel out x in both numerator and denominator.

$$\frac{-7x^{6}}{9}\times \frac{81x^{4}}{49}$$

Multiply \frac{-7x^{6}}{9} times \frac{81x^{4}}{49} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-7x^{6}\times 81x^{4}}{9\times 49}$$

Cancel out 7\times 9 in both numerator and denominator.

$$\frac{-9x^{4}x^{6}}{7}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{-9x^{10}}{7}$$

Differentiate w.r.t. x

$$-\frac{90x^{9}}{7}$$