Solve a^5b^2/a^4b^2=

$$\frac { a ^ { 5 } b ^ { 2 } } { a ^ { 4 } b ^ { 2 } } =$$

Evaluate

$$a$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{a^{5}b^{2}}{a^{4}b^{2}}$$

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

$$a^{5-4}b^{2-2}$$

Subtract 4 from 5.

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

Subtract 2 from 2.

$$a^{1}b^{0}$$

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

$$a$$

Differentiate w.r.t. a

$$1$$

Steps Using Definition of a Derivative

Cancel out b^{2}a^{4} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a)$$

The derivative of ax^{n} is nax^{n-1}.

$$a^{1-1}$$

Subtract 1 from 1.

$$a^{0}$$

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

$$1$$