Solve 8a^2b^2/2ab^2=

$$\frac { 8 a ^ { 2 } b ^ { 2 } } { 2 a b ^ { 2 } } =$$

Evaluate

$$4a$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}a^{2}b^{2}}{2^{1}a^{1}b^{2}}$$

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

$$\frac{8^{1}}{2^{1}}a^{2-1}b^{2-2}$$

Subtract 1 from 2.

$$\frac{8^{1}}{2^{1}}a^{1}b^{2-2}$$

Subtract 2 from 2.

$$\frac{8^{1}}{2^{1}}ab^{0}$$

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

$$\frac{8^{1}}{2^{1}}a$$

Divide 8 by 2.

$$4a$$

Differentiate w.r.t. a

$$4$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8b^{2}}{2b^{2}}a^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{1})$$

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}.

$$4a^{1-1}$$

Do the arithmetic.

$$4a^{0}$$

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

$$4\times 1$$

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

$$4$$