Solve -100x^4/10x^2=

$$\frac { - 100 x ^ { 4 } } { 10 x ^ { 2 } } =$$

Evaluate

$$-10x^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-100x^{4}\right)^{1}\times \frac{1}{10x^{2}}$$

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

$$\left(-100\right)^{1}\left(x^{4}\right)^{1}\times \frac{1}{10}\times \frac{1}{x^{2}}$$

Use the Commutative Property of Multiplication.

$$\left(-100\right)^{1}\times \frac{1}{10}\left(x^{4}\right)^{1}\times \frac{1}{x^{2}}$$

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

$$\left(-100\right)^{1}\times \frac{1}{10}x^{4}x^{2\left(-1\right)}$$

Multiply 2 times -1.

$$\left(-100\right)^{1}\times \frac{1}{10}x^{4}x^{-2}$$

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

$$\left(-100\right)^{1}\times \frac{1}{10}x^{4-2}$$

Add the exponents 4 and -2.

$$\left(-100\right)^{1}\times \frac{1}{10}x^{2}$$

Raise -100 to the power 1.

$$-100\times \frac{1}{10}x^{2}$$

Multiply -100 times \frac{1}{10}.

$$-10x^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-100\right)^{1}x^{4}}{10^{1}x^{2}}$$

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

$$\frac{\left(-100\right)^{1}x^{4-2}}{10^{1}}$$

Subtract 2 from 4.

$$\frac{\left(-100\right)^{1}x^{2}}{10^{1}}$$

Divide -100 by 10.

$$-10x^{2}$$

Differentiate w.r.t. x

$$-20x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{100}{10}\right)x^{4-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10x^{2})$$

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}.

$$2\left(-10\right)x^{2-1}$$

Do the arithmetic.

$$-20x^{1}$$

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

$$-20x$$