Solve 30a^9b^2/2a^6b^2

$$\frac { 30 a ^ { 9 } b ^ { 2 } } { 2 a ^ { 6 } b ^ { 2 } }$$

Evaluate

$$15a^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{30^{1}a^{9}b^{2}}{2^{1}a^{6}b^{2}}$$

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

$$\frac{30^{1}}{2^{1}}a^{9-6}b^{2-2}$$

Subtract 6 from 9.

$$\frac{30^{1}}{2^{1}}a^{3}b^{2-2}$$

Subtract 2 from 2.

$$\frac{30^{1}}{2^{1}}a^{3}b^{0}$$

For any number a except 0, a^{0}=1.

$$\frac{30^{1}}{2^{1}}a^{3}$$

Divide 30 by 2.

$$15a^{3}$$

Differentiate w.r.t. a

$$45a^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{30b^{2}}{2b^{2}}a^{9-6})$$

Do the arithmetic.

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

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}.

$$3\times 15a^{3-1}$$

Do the arithmetic.

$$45a^{2}$$