Solve (x^4)^5*x^9/x^12=

$$\frac { ( x ^ { 4 } ) ^ { 5 } \cdot x ^ { 9 } } { x ^ { 12 } } =$$

Evaluate

$$x^{17}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{x^{20}x^{9}}{x^{12}}$$

To multiply powers of the same base, add their exponents. Add 20 and 9 to get 29.

$$\frac{x^{29}}{x^{12}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 29 to get 17.

$$x^{17}$$

Differentiate w.r.t. x

$$17x^{16}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{20}x^{9}}{x^{12}})$$

To multiply powers of the same base, add their exponents. Add 20 and 9 to get 29.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{29}}{x^{12}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 29 to get 17.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{17})$$

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

$$17x^{17-1}$$

Subtract 1 from 17.

$$17x^{16}$$