Solve 10x^12/2x^4

$$\frac { 10 x ^ { 12 } } { 2 x ^ { 4 } }$$

Evaluate

$$5x^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(10x^{12}\right)^{1}\times \frac{1}{2x^{4}}$$

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

$$10^{1}\left(x^{12}\right)^{1}\times \frac{1}{2}\times \frac{1}{x^{4}}$$

Use the Commutative Property of Multiplication.

$$10^{1}\times \frac{1}{2}\left(x^{12}\right)^{1}\times \frac{1}{x^{4}}$$

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

$$10^{1}\times \frac{1}{2}x^{12}x^{4\left(-1\right)}$$

Multiply 4 times -1.

$$10^{1}\times \frac{1}{2}x^{12}x^{-4}$$

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

$$10^{1}\times \frac{1}{2}x^{12-4}$$

Add the exponents 12 and -4.

$$10^{1}\times \frac{1}{2}x^{8}$$

Raise 10 to the power 1.

$$10\times \frac{1}{2}x^{8}$$

Multiply 10 times \frac{1}{2}.

$$5x^{8}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}x^{12}}{2^{1}x^{4}}$$

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

$$\frac{10^{1}x^{12-4}}{2^{1}}$$

Subtract 4 from 12.

$$\frac{10^{1}x^{8}}{2^{1}}$$

Divide 10 by 2.

$$5x^{8}$$

Differentiate w.r.t. x

$$40x^{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10}{2}x^{12-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{8})$$

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}.

$$8\times 5x^{8-1}$$

Do the arithmetic.

$$40x^{7}$$