Solve 8a^30diva^3

$$8 a ^ { 30 } \div a ^ { 3 }$$

Evaluate

$$8a^{27}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8a^{30}\right)^{1}\times \frac{1}{a^{3}}$$

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

$$8^{1}\left(a^{30}\right)^{1}\times \frac{1}{1}\times \frac{1}{a^{3}}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \frac{1}{1}\left(a^{30}\right)^{1}\times \frac{1}{a^{3}}$$

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

$$8^{1}\times \frac{1}{1}a^{30}a^{3\left(-1\right)}$$

Multiply 3 times -1.

$$8^{1}\times \frac{1}{1}a^{30}a^{-3}$$

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

$$8^{1}\times \frac{1}{1}a^{30-3}$$

Add the exponents 30 and -3.

$$8^{1}\times \frac{1}{1}a^{27}$$

Raise 8 to the power 1.

$$8\times \frac{1}{1}a^{27}$$

Differentiate w.r.t. a

$$216a^{26}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8}{1}a^{30-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(8a^{27})$$

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}.

$$27\times 8a^{27-1}$$

Do the arithmetic.

$$216a^{26}$$