Solve 6a^7b^-2div36a^3b^-4

$$6 a ^ { 7 } b ^ { - 2 } \div 36 a ^ { 3 } b ^ { - 4 }$$

Evaluate

$$\frac{a^{10}}{6b^{6}}$$

Solution Steps

Divide 6a^{7}b^{-2} by 36 to get \frac{1}{6}a^{7}b^{-2}.

$$\frac{1}{6}a^{7}b^{-2}a^{3}b^{-4}$$

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$\frac{1}{6}a^{10}b^{-2}b^{-4}$$

To multiply powers of the same base, add their exponents. Add -2 and -4 to get -6.

$$\frac{1}{6}a^{10}b^{-6}$$

Differentiate w.r.t. a

$$\frac{5a^{9}}{3b^{6}}$$