Solve (15a^3b^2)div(3a^2b)=

$$( 15 a ^ { 3 } b ^ { 2 } ) \div ( 3 a ^ { 2 } b ) =$$

Evaluate

$$5ab$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{15^{1}a^{3}b^{2}}{3^{1}a^{2}b^{1}}$$

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

$$\frac{15^{1}}{3^{1}}a^{3-2}b^{2-1}$$

Subtract 2 from 3.

$$\frac{15^{1}}{3^{1}}a^{1}b^{2-1}$$

Subtract 1 from 2.

$$\frac{15^{1}}{3^{1}}ab^{1}$$

Divide 15 by 3.

$$5ab$$

Differentiate w.r.t. a

$$5b$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{15b^{2}}{3b}a^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5ba^{1})$$

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}.

$$5ba^{1-1}$$

Do the arithmetic.

$$5ba^{0}$$

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

$$5b\times 1$$

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

$$5b$$