Solve (x^7)^5*x^2/x^12=

$$\frac { ( x ^ { 7 } ) ^ { 5 } \cdot x ^ { 2 } } { x ^ { 12 } } =$$

Evaluate

$$x^{25}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 7 and 5 to get 35.

$$\frac{x^{35}x^{2}}{x^{12}}$$

To multiply powers of the same base, add their exponents. Add 35 and 2 to get 37.

$$\frac{x^{37}}{x^{12}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 37 to get 25.

$$x^{25}$$

Differentiate w.r.t. x

$$25x^{24}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 7 and 5 to get 35.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{35}x^{2}}{x^{12}})$$

To multiply powers of the same base, add their exponents. Add 35 and 2 to get 37.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{37}}{x^{12}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 37 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{25})$$

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

$$25x^{25-1}$$

Subtract 1 from 25.

$$25x^{24}$$