Solve frac{7a^{2}b^-3*3a^-3b^0}{14a^-1b}

$$\frac { 7 a ^ { 2 } b ^ { - 3 } \times 3 a ^ { - 3 } b ^ { 0 } } { 14 a ^ { - 1 } b }$$

Evaluate

$$\frac{3}{2b^{4}}$$

Solution Steps

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

$$\frac{7a^{-1}b^{-3}\times 3b^{0}}{14a^{-1}b}$$

To multiply powers of the same base, add their exponents. Add -3 and 0 to get -3.

$$\frac{7a^{-1}b^{-3}\times 3}{14a^{-1}b}$$

Cancel out 7\times \frac{1}{a} in both numerator and denominator.

$$\frac{3b^{-3}}{2b}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{3}{2b^{4}}$$

Differentiate w.r.t. b

$$-\frac{6}{b^{5}}$$