Solve 10x^-0/5x^-4

$$\frac { 10 x ^ { - 0 } } { 5 x ^ { - 4 } }$$

Evaluate

$$2x^{4}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(10x^{0}\right)^{1}\times \frac{1}{5x^{-4}}$$

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

$$10^{1}\left(x^{0}\right)^{1}\times \frac{1}{5}\times \frac{1}{x^{-4}}$$

Use the Commutative Property of Multiplication.

$$10^{1}\times \frac{1}{5}\left(x^{0}\right)^{1}\times \frac{1}{x^{-4}}$$

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

$$10^{1}\times \frac{1}{5}x^{0}x^{-4\left(-1\right)}$$

Multiply -4 times -1.

$$10^{1}\times \frac{1}{5}x^{0}x^{4}$$

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

$$10^{1}\times \frac{1}{5}x^{4}$$

Raise 10 to the power 1.

$$10\times \frac{1}{5}x^{4}$$

Multiply 10 times \frac{1}{5}.

$$2x^{4}$$

Differentiate w.r.t. x

$$8x^{3}$$

Steps Using Definition of a Derivative

Cancel out 5 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{0}}{x^{-4}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4})$$

The derivative of ax^{n} is nax^{n-1}.

$$4\times 2x^{4-1}$$

Multiply 4 times 2.

$$8x^{4-1}$$

Subtract 1 from 4.

$$8x^{3}$$