Solve (2a)/2a^-2

$$\frac { ( 2 a ) } { 2 a ^ { - 2 } }$$

Evaluate

$$a^{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply -2 times -1.

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

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

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

Add the exponents 1 and 2.

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

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

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

Add the exponents 1 and -1.

$$2^{0}a^{3}$$

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

$$1a^{3}$$

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

$$a^{3}$$

Differentiate w.r.t. a

$$3a^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2}{2}a^{1-\left(-2\right)})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$3a^{2}$$