Solve 12a^7/4a^2=

$$\frac { 12 a ^ { 7 } } { 4 a ^ { 2 } } =$$

Evaluate

$$3a^{5}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(12a^{7}\right)^{1}\times \frac{1}{4a^{2}}$$

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

$$12^{1}\left(a^{7}\right)^{1}\times \frac{1}{4}\times \frac{1}{a^{2}}$$

Use the Commutative Property of Multiplication.

$$12^{1}\times \frac{1}{4}\left(a^{7}\right)^{1}\times \frac{1}{a^{2}}$$

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

$$12^{1}\times \frac{1}{4}a^{7}a^{2\left(-1\right)}$$

Multiply 2 times -1.

$$12^{1}\times \frac{1}{4}a^{7}a^{-2}$$

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

$$12^{1}\times \frac{1}{4}a^{7-2}$$

Add the exponents 7 and -2.

$$12^{1}\times \frac{1}{4}a^{5}$$

Raise 12 to the power 1.

$$12\times \frac{1}{4}a^{5}$$

Multiply 12 times \frac{1}{4}.

$$3a^{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}a^{7}}{4^{1}a^{2}}$$

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

$$\frac{12^{1}a^{7-2}}{4^{1}}$$

Subtract 2 from 7.

$$\frac{12^{1}a^{5}}{4^{1}}$$

Divide 12 by 4.

$$3a^{5}$$

Differentiate w.r.t. a

$$15a^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{12}{4}a^{7-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{5})$$

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}.

$$5\times 3a^{5-1}$$

Do the arithmetic.

$$15a^{4}$$