Solve 2a^6/6a^5

$$\frac { 2 a ^ { 6 } } { 6 a ^ { 5 } }$$

Evaluate

$$\frac{a}{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2a^{6}\right)^{1}\times \frac{1}{6a^{5}}$$

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

$$2^{1}\left(a^{6}\right)^{1}\times \frac{1}{6}\times \frac{1}{a^{5}}$$

Use the Commutative Property of Multiplication.

$$2^{1}\times \frac{1}{6}\left(a^{6}\right)^{1}\times \frac{1}{a^{5}}$$

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

$$2^{1}\times \frac{1}{6}a^{6}a^{5\left(-1\right)}$$

Multiply 5 times -1.

$$2^{1}\times \frac{1}{6}a^{6}a^{-5}$$

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

$$2^{1}\times \frac{1}{6}a^{6-5}$$

Add the exponents 6 and -5.

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

Raise 2 to the power 1.

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

Multiply 2 times \frac{1}{6}.

$$\frac{1}{3}a^{1}$$

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

$$\frac{1}{3}a$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}a^{6}}{6^{1}a^{5}}$$

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

$$\frac{2^{1}a^{6-5}}{6^{1}}$$

Subtract 5 from 6.

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

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}a^{1}$$

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

$$\frac{1}{3}a$$

Differentiate w.r.t. a

$$\frac{1}{3} = 0.3333333333333333$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2}{6}a^{6-5})$$

Do the arithmetic.

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

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}.

$$\frac{1}{3}a^{1-1}$$

Do the arithmetic.

$$\frac{1}{3}a^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{3}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{3}$$