Solve 2a^6diva^4

$$2 a ^ { 6 } \div a ^ { 4 }$$

Evaluate

$$2a^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2a^{6}\right)^{1}\times \frac{1}{a^{4}}$$

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

$$2^{1}\left(a^{6}\right)^{1}\times \frac{1}{1}\times \frac{1}{a^{4}}$$

Use the Commutative Property of Multiplication.

$$2^{1}\times \frac{1}{1}\left(a^{6}\right)^{1}\times \frac{1}{a^{4}}$$

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

$$2^{1}\times \frac{1}{1}a^{6}a^{4\left(-1\right)}$$

Multiply 4 times -1.

$$2^{1}\times \frac{1}{1}a^{6}a^{-4}$$

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

$$2^{1}\times \frac{1}{1}a^{6-4}$$

Add the exponents 6 and -4.

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

Raise 2 to the power 1.

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

Differentiate w.r.t. a

$$4a$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2}{1}a^{6-4})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$4a^{1}$$

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

$$4a$$