Solve 12x^8/6x^4

$$\frac { 12 x ^ { 8 } } { 6 x ^ { 4 } }$$

Evaluate

$$2x^{4}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(12x^{8}\right)^{1}\times \frac{1}{6x^{4}}$$

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

$$12^{1}\left(x^{8}\right)^{1}\times \frac{1}{6}\times \frac{1}{x^{4}}$$

Use the Commutative Property of Multiplication.

$$12^{1}\times \frac{1}{6}\left(x^{8}\right)^{1}\times \frac{1}{x^{4}}$$

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

$$12^{1}\times \frac{1}{6}x^{8}x^{4\left(-1\right)}$$

Multiply 4 times -1.

$$12^{1}\times \frac{1}{6}x^{8}x^{-4}$$

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

$$12^{1}\times \frac{1}{6}x^{8-4}$$

Add the exponents 8 and -4.

$$12^{1}\times \frac{1}{6}x^{4}$$

Raise 12 to the power 1.

$$12\times \frac{1}{6}x^{4}$$

Multiply 12 times \frac{1}{6}.

$$2x^{4}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}x^{8}}{6^{1}x^{4}}$$

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

$$\frac{12^{1}x^{8-4}}{6^{1}}$$

Subtract 4 from 8.

$$\frac{12^{1}x^{4}}{6^{1}}$$

Divide 12 by 6.

$$2x^{4}$$

Differentiate w.r.t. x

$$8x^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12}{6}x^{8-4})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$8x^{3}$$