Solve 10x^10/2x^7

$$\frac { 10 x ^ { 10 } } { 2 x ^ { 7 } }$$

Evaluate

$$5x^{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(10x^{10}\right)^{1}\times \frac{1}{2x^{7}}$$

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

$$10^{1}\left(x^{10}\right)^{1}\times \frac{1}{2}\times \frac{1}{x^{7}}$$

Use the Commutative Property of Multiplication.

$$10^{1}\times \frac{1}{2}\left(x^{10}\right)^{1}\times \frac{1}{x^{7}}$$

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

$$10^{1}\times \frac{1}{2}x^{10}x^{7\left(-1\right)}$$

Multiply 7 times -1.

$$10^{1}\times \frac{1}{2}x^{10}x^{-7}$$

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

$$10^{1}\times \frac{1}{2}x^{10-7}$$

Add the exponents 10 and -7.

$$10^{1}\times \frac{1}{2}x^{3}$$

Raise 10 to the power 1.

$$10\times \frac{1}{2}x^{3}$$

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

$$5x^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}x^{10}}{2^{1}x^{7}}$$

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

$$\frac{10^{1}x^{10-7}}{2^{1}}$$

Subtract 7 from 10.

$$\frac{10^{1}x^{3}}{2^{1}}$$

Divide 10 by 2.

$$5x^{3}$$

Differentiate w.r.t. x

$$15x^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10}{2}x^{10-7})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3})$$

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}.

$$3\times 5x^{3-1}$$

Do the arithmetic.

$$15x^{2}$$