Solve y^16/y^6

$$\frac { y ^ { 16 } } { y ^ { 6 } }$$

Evaluate

$$y^{10}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{16}}{y^{6}}$$

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

$$y^{16-6}$$

Subtract 6 from 16.

$$y^{10}$$

Differentiate w.r.t. y

$$10y^{9}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{16-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{10})$$

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}.

$$10y^{10-1}$$

Do the arithmetic.

$$10y^{9}$$