Solve 8a^4/12a^-7

$$\frac { 8 a ^ { 4 } } { 12 a ^ { - 7 } }$$

Evaluate

$$\frac{2a^{11}}{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8a^{4}\right)^{1}\times \frac{1}{12a^{-7}}$$

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

$$8^{1}\left(a^{4}\right)^{1}\times \frac{1}{12}\times \frac{1}{a^{-7}}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \frac{1}{12}\left(a^{4}\right)^{1}\times \frac{1}{a^{-7}}$$

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

$$8^{1}\times \frac{1}{12}a^{4}a^{-7\left(-1\right)}$$

Multiply -7 times -1.

$$8^{1}\times \frac{1}{12}a^{4}a^{7}$$

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

$$8^{1}\times \frac{1}{12}a^{4+7}$$

Add the exponents 4 and 7.

$$8^{1}\times \frac{1}{12}a^{11}$$

Raise 8 to the power 1.

$$8\times \frac{1}{12}a^{11}$$

Multiply 8 times \frac{1}{12}.

$$\frac{2}{3}a^{11}$$

Differentiate w.r.t. a

$$\frac{22a^{10}}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8}{12}a^{4-\left(-7\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2}{3}a^{11})$$

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}.

$$11\times \frac{2}{3}a^{11-1}$$

Do the arithmetic.

$$\frac{22}{3}a^{10}$$