Solve 20x^7/5x^5

$$\frac { 20 x ^ { 7 } } { 5 x ^ { 5 } }$$

Evaluate

$$4x^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(20x^{7}\right)^{1}\times \frac{1}{5x^{5}}$$

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

$$20^{1}\left(x^{7}\right)^{1}\times \frac{1}{5}\times \frac{1}{x^{5}}$$

Use the Commutative Property of Multiplication.

$$20^{1}\times \frac{1}{5}\left(x^{7}\right)^{1}\times \frac{1}{x^{5}}$$

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

$$20^{1}\times \frac{1}{5}x^{7}x^{5\left(-1\right)}$$

Multiply 5 times -1.

$$20^{1}\times \frac{1}{5}x^{7}x^{-5}$$

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

$$20^{1}\times \frac{1}{5}x^{7-5}$$

Add the exponents 7 and -5.

$$20^{1}\times \frac{1}{5}x^{2}$$

Raise 20 to the power 1.

$$20\times \frac{1}{5}x^{2}$$

Multiply 20 times \frac{1}{5}.

$$4x^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{20^{1}x^{7}}{5^{1}x^{5}}$$

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

$$\frac{20^{1}x^{7-5}}{5^{1}}$$

Subtract 5 from 7.

$$\frac{20^{1}x^{2}}{5^{1}}$$

Divide 20 by 5.

$$4x^{2}$$

Differentiate w.r.t. x

$$8x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20}{5}x^{7-5})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$8x^{1}$$

For any term t, t^{1}=t.

$$8x$$