Solve (a^-1)^-1

$$( a ^ { - 1 } ) ^ { - 1 }$$

Evaluate

$$a$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

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

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

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

Multiply -1 times -1.

$$a$$

Steps for Raising Quotient to a Power

Use the rules of exponents to simplify the expression.

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

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

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

Differentiate w.r.t. a

$$1$$

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).

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

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}.

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

Simplify.

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