Solve 1/y^9*y^15

$$\frac { 1 } { y ^ { 9 } } \cdot y ^ { 15 }$$

Evaluate

$$y^{6}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{15}}{y^{9}}$$

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

$$y^{15-9}$$

Subtract 9 from 15.

$$y^{6}$$

Differentiate w.r.t. y

$$6y^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{15-9})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{6})$$

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}.

$$6y^{6-1}$$

Do the arithmetic.

$$6y^{5}$$