Solve 256x^2/2^8a^8*10b/25ab=

$$\frac { 256 x ^ { 2 } } { 2 ^ { 8 } a ^ { 8 } } \times \frac { 10 b } { 25 a b } =$$

Evaluate

$$\frac{2x^{2}}{5a^{9}}$$

Solution Steps

Calculate 2 to the power of 8 and get 256.

$$\frac{256x^{2}}{256a^{8}}\times \frac{10b}{25ab}$$

Cancel out 256 in both numerator and denominator.

$$\frac{x^{2}}{a^{8}}\times \frac{10b}{25ab}$$

Cancel out 5b in both numerator and denominator.

$$\frac{x^{2}}{a^{8}}\times \frac{2}{5a}$$

Multiply \frac{x^{2}}{a^{8}} times \frac{2}{5a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}\times 2}{a^{8}\times 5a}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$\frac{x^{2}\times 2}{a^{9}\times 5}$$

Differentiate w.r.t. x

$$\frac{4x}{5a^{9}}$$