Solve (a^-2b^-2/20)div6a^3b^2

$$( \frac { a ^ { - 2 } b ^ { - 2 } } { 20 } ) \div 6 a ^ { 3 } b ^ { 2 }$$

Evaluate

$$\frac{a}{120}$$

Solution Steps

Express \frac{\frac{a^{-2}b^{-2}}{20}}{6} as a single fraction.

$$\frac{a^{-2}b^{-2}}{20\times 6}a^{3}b^{2}$$

Multiply 20 and 6 to get 120.

$$\frac{a^{-2}b^{-2}}{120}a^{3}b^{2}$$

Express \frac{a^{-2}b^{-2}}{120}a^{3} as a single fraction.

$$\frac{a^{-2}b^{-2}a^{3}}{120}b^{2}$$

Express \frac{a^{-2}b^{-2}a^{3}}{120}b^{2} as a single fraction.

$$\frac{a^{-2}b^{-2}a^{3}b^{2}}{120}$$

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

$$\frac{a^{1}b^{-2}b^{2}}{120}$$

Multiply b^{-2} and b^{2} to get 1.

$$\frac{a^{1}}{120}$$

Calculate a to the power of 1 and get a.

$$\frac{a}{120}$$

Differentiate w.r.t. a

$$\frac{1}{120} = 0.008333333333333333$$

Steps Using Definition of a Derivative

Express \frac{\frac{a^{-2}b^{-2}}{20}}{6} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{-2}b^{-2}}{20\times 6}a^{3}b^{2})$$

Multiply 20 and 6 to get 120.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{-2}b^{-2}}{120}a^{3}b^{2})$$

Express \frac{a^{-2}b^{-2}}{120}a^{3} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{-2}b^{-2}a^{3}}{120}b^{2})$$

Express \frac{a^{-2}b^{-2}a^{3}}{120}b^{2} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{-2}b^{-2}a^{3}b^{2}}{120})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{1}b^{-2}b^{2}}{120})$$

Multiply b^{-2} and b^{2} to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{1}}{120})$$

Calculate a to the power of 1 and get a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a}{120})$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{120}a^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{120}a^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{120}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{120}$$