Solve 6a^2b^2/3ab^4=

$$\frac { 6 a ^ { 2 } b ^ { 2 } } { 3 a b ^ { 4 } } =$$

Evaluate

$$\frac{2a}{b^{2}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 1 from 2.

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

Subtract 4 from 2.

$$\frac{6^{1}}{3^{1}}ab^{-2}$$

Divide 6 by 3.

$$2a\times \frac{1}{b^{2}}$$

Differentiate w.r.t. a

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{6b^{2}}{3b^{4}}a^{2-1})$$

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

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

Do the arithmetic.

$$\frac{2}{b^{2}}a^{0}$$

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

$$\frac{2}{b^{2}}\times 1$$

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

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