Solve (x^9)^3/x^6

$$\frac { ( x ^ { 9 } ) ^ { 3 } } { x ^ { 6 } }$$

Evaluate

$$x^{21}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(x^{9}\right)^{3}\times \frac{1}{x^{6}}$$

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

$$x^{9\times 3}x^{6\left(-1\right)}$$

Multiply 9 times 3.

$$x^{27}x^{6\left(-1\right)}$$

Multiply 6 times -1.

$$x^{27}x^{-6}$$

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

$$x^{27-6}$$

Add the exponents 27 and -6.

$$x^{21}$$

Differentiate w.r.t. x

$$21x^{20}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{27}}{x^{6}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 27 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{21})$$

The derivative of ax^{n} is nax^{n-1}.

$$21x^{21-1}$$

Subtract 1 from 21.

$$21x^{20}$$