Solve 8a^9/2a^4

$$\frac { 8 a ^ { 9 } } { 2 a ^ { 4 } }$$

Evaluate

$$4a^{5}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8a^{9}\right)^{1}\times \frac{1}{2a^{4}}$$

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

$$8^{1}\left(a^{9}\right)^{1}\times \frac{1}{2}\times \frac{1}{a^{4}}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \frac{1}{2}\left(a^{9}\right)^{1}\times \frac{1}{a^{4}}$$

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

$$8^{1}\times \frac{1}{2}a^{9}a^{4\left(-1\right)}$$

Multiply 4 times -1.

$$8^{1}\times \frac{1}{2}a^{9}a^{-4}$$

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

$$8^{1}\times \frac{1}{2}a^{9-4}$$

Add the exponents 9 and -4.

$$8^{1}\times \frac{1}{2}a^{5}$$

Raise 8 to the power 1.

$$8\times \frac{1}{2}a^{5}$$

Multiply 8 times \frac{1}{2}.

$$4a^{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}a^{9}}{2^{1}a^{4}}$$

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

$$\frac{8^{1}a^{9-4}}{2^{1}}$$

Subtract 4 from 9.

$$\frac{8^{1}a^{5}}{2^{1}}$$

Divide 8 by 2.

$$4a^{5}$$

Differentiate w.r.t. a

$$20a^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8}{2}a^{9-4})$$

Do the arithmetic.

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

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}.

$$5\times 4a^{5-1}$$

Do the arithmetic.

$$20a^{4}$$