Solve (-a)^0/2a^5

$$\frac { ( - a ) ^ { 0 } } { 2 a ^ { 5 } }$$

Evaluate

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

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-a^{1}\right)^{0}\times \frac{1}{2a^{5}}$$

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

$$\left(a^{1}\right)^{0}\times \frac{1}{2}\times \frac{1}{a^{5}}$$

Use the Commutative Property of Multiplication.

$$\frac{1}{2}\left(a^{1}\right)^{0}\times \frac{1}{a^{5}}$$

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

$$\frac{1}{2}a^{0}a^{5\left(-1\right)}$$

Multiply 5 times -1.

$$\frac{1}{2}a^{0}a^{-5}$$

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

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

Differentiate w.r.t. a

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

Steps Using Chain Rule

Calculate -a to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{2a^{5}})$$

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).

$$-\left(2a^{5}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}a}(2a^{5})$$

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}.

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

Simplify.

$$-10a^{4}\times \left(2a^{5}\right)^{-2}$$