Solve 8y^10/3y^6

$$\frac { 8 y ^ { 10 } } { 3 y ^ { 6 } }$$

Evaluate

$$\frac{8y^{4}}{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8y^{10}\right)^{1}\times \frac{1}{3y^{6}}$$

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

$$8^{1}\left(y^{10}\right)^{1}\times \frac{1}{3}\times \frac{1}{y^{6}}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \frac{1}{3}\left(y^{10}\right)^{1}\times \frac{1}{y^{6}}$$

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

$$8^{1}\times \frac{1}{3}y^{10}y^{6\left(-1\right)}$$

Multiply 6 times -1.

$$8^{1}\times \frac{1}{3}y^{10}y^{-6}$$

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

$$8^{1}\times \frac{1}{3}y^{10-6}$$

Add the exponents 10 and -6.

$$8^{1}\times \frac{1}{3}y^{4}$$

Raise 8 to the power 1.

$$8\times \frac{1}{3}y^{4}$$

Multiply 8 times \frac{1}{3}.

$$\frac{8}{3}y^{4}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}y^{10}}{3^{1}y^{6}}$$

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

$$\frac{8^{1}y^{10-6}}{3^{1}}$$

Subtract 6 from 10.

$$\frac{8^{1}y^{4}}{3^{1}}$$

Divide 8 by 3.

$$\frac{8}{3}y^{4}$$

Differentiate w.r.t. y

$$\frac{32y^{3}}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{8}{3}y^{10-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{8}{3}y^{4})$$

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}.

$$4\times \frac{8}{3}y^{4-1}$$

Do the arithmetic.

$$\frac{32}{3}y^{3}$$