Solve 9y^3/10y^2

$$\frac { 9 y ^ { 3 } } { 10 y ^ { 2 } }$$

Evaluate

$$\frac{9y}{10}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(9y^{3}\right)^{1}\times \frac{1}{10y^{2}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$9^{1}\left(y^{3}\right)^{1}\times \frac{1}{10}\times \frac{1}{y^{2}}$$

Use the Commutative Property of Multiplication.

$$9^{1}\times \frac{1}{10}\left(y^{3}\right)^{1}\times \frac{1}{y^{2}}$$

To raise a power to another power, multiply the exponents.

$$9^{1}\times \frac{1}{10}y^{3}y^{2\left(-1\right)}$$

Multiply 2 times -1.

$$9^{1}\times \frac{1}{10}y^{3}y^{-2}$$

To multiply powers of the same base, add their exponents.

$$9^{1}\times \frac{1}{10}y^{3-2}$$

Add the exponents 3 and -2.

$$9^{1}\times \frac{1}{10}y^{1}$$

Raise 9 to the power 1.

$$9\times \frac{1}{10}y^{1}$$

Multiply 9 times \frac{1}{10}.

$$\frac{9}{10}y^{1}$$

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

$$\frac{9}{10}y$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{9^{1}y^{3}}{10^{1}y^{2}}$$

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

$$\frac{9^{1}y^{3-2}}{10^{1}}$$

Subtract 2 from 3.

$$\frac{9^{1}y^{1}}{10^{1}}$$

Divide 9 by 10.

$$\frac{9}{10}y^{1}$$

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

$$\frac{9}{10}y$$

Differentiate w.r.t. y

$$\frac{9}{10} = 0.9$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{9}{10}y^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{9}{10}y^{1})$$

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}.

$$\frac{9}{10}y^{1-1}$$

Do the arithmetic.

$$\frac{9}{10}y^{0}$$

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

$$\frac{9}{10}\times 1$$

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

$$\frac{9}{10}$$