Solve x^6(x^-3/x^-10)^-1

$$x ^ { 6 } ( x ^ { - 3 } / x ^ { - 10 } ) ^ { - 1 }$$

Evaluate

$$\frac{1}{x}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -10 from -3 to get 7.

$$x^{6}\left(x^{7}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -1 to get -7.

$$x^{6}x^{-7}$$

To multiply powers of the same base, add their exponents. Add 6 and -7 to get -1.

$$x^{-1}$$

Differentiate w.r.t. x

$$-\frac{1}{x^{2}}$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -10 from -3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}\left(x^{7}\right)^{-1})$$

To raise a power to another power, multiply the exponents. Multiply 7 and -1 to get -7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}x^{-7})$$

To multiply powers of the same base, add their exponents. Add 6 and -7 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-1})$$

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

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

Subtract 1 from -1.

$$-x^{-2}$$