Solve frac{1}a^3

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

Evaluate

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

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{a}\right)^{3}$$

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

$$a^{-3}$$

Multiply -1 times 3.

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

Steps for Raising Quotient to a Power

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{a^{1}}\right)^{3}$$

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

$$\frac{1^{3}}{\left(a^{1}\right)^{3}}$$

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

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

Differentiate w.r.t. a

$$-\frac{3}{a^{4}}$$

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$3\times \left(\frac{1}{a}\right)^{3-1}\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{a})$$

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}.

$$3\times \left(\frac{1}{a}\right)^{2}\left(-1\right)a^{-1-1}$$

Simplify.

$$-3a^{-2}\times \left(\frac{1}{a}\right)^{2}$$