Solve y^32/y^2

$$\frac { y ^ { 32 } } { y ^ { 2 } }$$

Evaluate

$$y^{30}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{32}}{y^{2}}$$

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

$$y^{32-2}$$

Subtract 2 from 32.

$$y^{30}$$

Differentiate w.r.t. y

$$30y^{29}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{32-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{30})$$

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}.

$$30y^{30-1}$$

Do the arithmetic.

$$30y^{29}$$