Solve -108x^6/-12x^2

$$\frac{ -108 { x }^{ 6 } }{ -12 { x }^{ 2 } }$$

Evaluate

$$9x^{4}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-108x^{6}\right)^{1}\times \frac{1}{-12x^{2}}$$

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

$$\left(-108\right)^{1}\left(x^{6}\right)^{1}\times \frac{1}{-12}\times \frac{1}{x^{2}}$$

Use the Commutative Property of Multiplication.

$$\left(-108\right)^{1}\times \frac{1}{-12}\left(x^{6}\right)^{1}\times \frac{1}{x^{2}}$$

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

$$\left(-108\right)^{1}\times \frac{1}{-12}x^{6}x^{2\left(-1\right)}$$

Multiply 2 times -1.

$$\left(-108\right)^{1}\times \frac{1}{-12}x^{6}x^{-2}$$

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

$$\left(-108\right)^{1}\times \frac{1}{-12}x^{6-2}$$

Add the exponents 6 and -2.

$$\left(-108\right)^{1}\times \frac{1}{-12}x^{4}$$

Raise -108 to the power 1.

$$-108\times \frac{1}{-12}x^{4}$$

Raise -12 to the power -1.

$$-108\left(-\frac{1}{12}\right)x^{4}$$

Multiply -108 times -\frac{1}{12}.

$$9x^{4}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-108\right)^{1}x^{6}}{\left(-12\right)^{1}x^{2}}$$

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

$$\frac{\left(-108\right)^{1}x^{6-2}}{\left(-12\right)^{1}}$$

Subtract 2 from 6.

$$\frac{\left(-108\right)^{1}x^{4}}{\left(-12\right)^{1}}$$

Divide -108 by -12.

$$9x^{4}$$

Differentiate w.r.t. x

$$36x^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{108}{-12}\right)x^{6-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{4})$$

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}.

$$4\times 9x^{4-1}$$

Do the arithmetic.

$$36x^{3}$$