Solve 18a^7/6a^5

$$\frac { 18 a ^ { 7 } } { 6 a ^ { 5 } }$$

Evaluate

$$3a^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(18a^{7}\right)^{1}\times \frac{1}{6a^{5}}$$

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

$$18^{1}\left(a^{7}\right)^{1}\times \frac{1}{6}\times \frac{1}{a^{5}}$$

Use the Commutative Property of Multiplication.

$$18^{1}\times \frac{1}{6}\left(a^{7}\right)^{1}\times \frac{1}{a^{5}}$$

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

$$18^{1}\times \frac{1}{6}a^{7}a^{5\left(-1\right)}$$

Multiply 5 times -1.

$$18^{1}\times \frac{1}{6}a^{7}a^{-5}$$

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

$$18^{1}\times \frac{1}{6}a^{7-5}$$

Add the exponents 7 and -5.

$$18^{1}\times \frac{1}{6}a^{2}$$

Raise 18 to the power 1.

$$18\times \frac{1}{6}a^{2}$$

Multiply 18 times \frac{1}{6}.

$$3a^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{18^{1}a^{7}}{6^{1}a^{5}}$$

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

$$\frac{18^{1}a^{7-5}}{6^{1}}$$

Subtract 5 from 7.

$$\frac{18^{1}a^{2}}{6^{1}}$$

Divide 18 by 6.

$$3a^{2}$$

Differentiate w.r.t. a

$$6a$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{18}{6}a^{7-5})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$6a^{1}$$

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

$$6a$$