Solve 9x^10/3x^5

$$\frac { 9 x ^ { 10 } } { 3 x ^ { 5 } }$$

Evaluate

$$3x^{5}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(9x^{10}\right)^{1}\times \frac{1}{3x^{5}}$$

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

$$9^{1}\left(x^{10}\right)^{1}\times \frac{1}{3}\times \frac{1}{x^{5}}$$

Use the Commutative Property of Multiplication.

$$9^{1}\times \frac{1}{3}\left(x^{10}\right)^{1}\times \frac{1}{x^{5}}$$

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

$$9^{1}\times \frac{1}{3}x^{10}x^{5\left(-1\right)}$$

Multiply 5 times -1.

$$9^{1}\times \frac{1}{3}x^{10}x^{-5}$$

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

$$9^{1}\times \frac{1}{3}x^{10-5}$$

Add the exponents 10 and -5.

$$9^{1}\times \frac{1}{3}x^{5}$$

Raise 9 to the power 1.

$$9\times \frac{1}{3}x^{5}$$

Multiply 9 times \frac{1}{3}.

$$3x^{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{9^{1}x^{10}}{3^{1}x^{5}}$$

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

$$\frac{9^{1}x^{10-5}}{3^{1}}$$

Subtract 5 from 10.

$$\frac{9^{1}x^{5}}{3^{1}}$$

Divide 9 by 3.

$$3x^{5}$$

Differentiate w.r.t. x

$$15x^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{3}x^{10-5})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$15x^{4}$$