Solve 1/2x^23/4x5/8x^3=

$$\frac { 1 } { 2 x ^ { 2 } } \frac { 3 } { 4 x } \frac { 5 } { 8 x ^ { 3 } } =$$

Evaluate

$$\frac{15}{64x^{6}}$$

Solution Steps

Multiply \frac{1}{2x^{2}} times \frac{3}{4x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2x^{2}\times 4x}\times \frac{5}{8x^{3}}$$

Multiply \frac{3}{2x^{2}\times 4x} times \frac{5}{8x^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 5}{2x^{2}\times 4x\times 8x^{3}}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{3\times 5}{2x^{3}\times 4\times 8x^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{3\times 5}{2x^{6}\times 4\times 8}$$

Multiply 3 and 5 to get 15.

$$\frac{15}{2x^{6}\times 4\times 8}$$

Multiply 2 and 4 to get 8.

$$\frac{15}{8x^{6}\times 8}$$

Multiply 8 and 8 to get 64.

$$\frac{15}{64x^{6}}$$

Differentiate w.r.t. x

$$-\frac{45}{32x^{7}}$$