Solve (39a^2b^2):(13ab)

$$( 39 a ^ { 2 } b ^ { 2 } ) : ( 13 a b )$$

Evaluate

$$3ab$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{39^{1}a^{2}b^{2}}{13^{1}a^{1}b^{1}}$$

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

$$\frac{39^{1}}{13^{1}}a^{2-1}b^{2-1}$$

Subtract 1 from 2.

$$\frac{39^{1}}{13^{1}}a^{1}b^{2-1}$$

Subtract 1 from 2.

$$\frac{39^{1}}{13^{1}}ab^{1}$$

Divide 39 by 13.

$$3ab$$

Differentiate w.r.t. a

$$3b$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{39b^{2}}{13b}a^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3ba^{1})$$

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}.

$$3ba^{1-1}$$

Do the arithmetic.

$$3ba^{0}$$

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

$$3b\times 1$$

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

$$3b$$