Solve (24x^12)div(3x^4)

$$( 24 x ^ { 12 } ) \div ( 3 x ^ { 4 } )$$

Evaluate

$$8x^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(24x^{12}\right)^{1}\times \frac{1}{3x^{4}}$$

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

$$24^{1}\left(x^{12}\right)^{1}\times \frac{1}{3}\times \frac{1}{x^{4}}$$

Use the Commutative Property of Multiplication.

$$24^{1}\times \frac{1}{3}\left(x^{12}\right)^{1}\times \frac{1}{x^{4}}$$

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

$$24^{1}\times \frac{1}{3}x^{12}x^{4\left(-1\right)}$$

Multiply 4 times -1.

$$24^{1}\times \frac{1}{3}x^{12}x^{-4}$$

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

$$24^{1}\times \frac{1}{3}x^{12-4}$$

Add the exponents 12 and -4.

$$24^{1}\times \frac{1}{3}x^{8}$$

Raise 24 to the power 1.

$$24\times \frac{1}{3}x^{8}$$

Multiply 24 times \frac{1}{3}.

$$8x^{8}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{24^{1}x^{12}}{3^{1}x^{4}}$$

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

$$\frac{24^{1}x^{12-4}}{3^{1}}$$

Subtract 4 from 12.

$$\frac{24^{1}x^{8}}{3^{1}}$$

Divide 24 by 3.

$$8x^{8}$$

Differentiate w.r.t. x

$$64x^{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{3}x^{12-4})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$64x^{7}$$