Solve 5a^4/10a^2=

$$\frac { 5 a ^ { 4 } } { 10 a ^ { 2 } } =$$

Evaluate

$$\frac{a^{2}}{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(5a^{4}\right)^{1}\times \frac{1}{10a^{2}}$$

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

$$5^{1}\left(a^{4}\right)^{1}\times \frac{1}{10}\times \frac{1}{a^{2}}$$

Use the Commutative Property of Multiplication.

$$5^{1}\times \frac{1}{10}\left(a^{4}\right)^{1}\times \frac{1}{a^{2}}$$

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

$$5^{1}\times \frac{1}{10}a^{4}a^{2\left(-1\right)}$$

Multiply 2 times -1.

$$5^{1}\times \frac{1}{10}a^{4}a^{-2}$$

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

$$5^{1}\times \frac{1}{10}a^{4-2}$$

Add the exponents 4 and -2.

$$5^{1}\times \frac{1}{10}a^{2}$$

Raise 5 to the power 1.

$$5\times \frac{1}{10}a^{2}$$

Multiply 5 times \frac{1}{10}.

$$\frac{1}{2}a^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{5^{1}a^{4}}{10^{1}a^{2}}$$

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

$$\frac{5^{1}a^{4-2}}{10^{1}}$$

Subtract 2 from 4.

$$\frac{5^{1}a^{2}}{10^{1}}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}a^{2}$$

Differentiate w.r.t. a

$$a$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5}{10}a^{4-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{2}a^{2})$$

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}.

$$2\times \frac{1}{2}a^{2-1}$$

Do the arithmetic.

$$a^{1}$$

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

$$a$$