Solve 1/2a^4b^4div1/4a^5b^6=

$$\frac { 1 } { 2 } a ^ { 4 } b ^ { 4 } \div \frac { 1 } { 4 } a ^ { 5 } b ^ { 6 } =$$

Evaluate

$$2a^{9}b^{10}$$

Solution Steps

Divide \frac{1}{2}a^{4}b^{4} by \frac{1}{4} by multiplying \frac{1}{2}a^{4}b^{4} by the reciprocal of \frac{1}{4}.

$$\frac{1}{2}a^{4}b^{4}\times 4a^{5}b^{6}$$

Multiply \frac{1}{2} and 4 to get 2.

$$2a^{4}b^{4}a^{5}b^{6}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$2a^{9}b^{4}b^{6}$$

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

$$2a^{9}b^{10}$$

Differentiate w.r.t. a

$$18a^{8}b^{10}$$