Solve 10y^6/2y^4

$$\frac { 10 y ^ { 6 } } { 2 y ^ { 4 } }$$

Evaluate

$$5y^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(10y^{6}\right)^{1}\times \frac{1}{2y^{4}}$$

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

$$10^{1}\left(y^{6}\right)^{1}\times \frac{1}{2}\times \frac{1}{y^{4}}$$

Use the Commutative Property of Multiplication.

$$10^{1}\times \frac{1}{2}\left(y^{6}\right)^{1}\times \frac{1}{y^{4}}$$

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

$$10^{1}\times \frac{1}{2}y^{6}y^{4\left(-1\right)}$$

Multiply 4 times -1.

$$10^{1}\times \frac{1}{2}y^{6}y^{-4}$$

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

$$10^{1}\times \frac{1}{2}y^{6-4}$$

Add the exponents 6 and -4.

$$10^{1}\times \frac{1}{2}y^{2}$$

Raise 10 to the power 1.

$$10\times \frac{1}{2}y^{2}$$

Multiply 10 times \frac{1}{2}.

$$5y^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}y^{6}}{2^{1}y^{4}}$$

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

$$\frac{10^{1}y^{6-4}}{2^{1}}$$

Subtract 4 from 6.

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

Divide 10 by 2.

$$5y^{2}$$

Differentiate w.r.t. y

$$10y$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{10}{2}y^{6-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(5y^{2})$$

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}.

$$2\times 5y^{2-1}$$

Do the arithmetic.

$$10y^{1}$$

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

$$10y$$