Solve (x^-2)^5*x^7=

$$( x ^ { - 2 } ) ^ { 5 } \times x ^ { 7 } =$$

Evaluate

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and 5 to get -10.

$$x^{-10}x^{7}$$

To multiply powers of the same base, add their exponents. Add -10 and 7 to get -3.

$$x^{-3}$$

Differentiate w.r.t. x

$$-\frac{3}{x^{4}}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply -2 and 5 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-10}x^{7})$$

To multiply powers of the same base, add their exponents. Add -10 and 7 to get -3.

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

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

$$-3x^{-3-1}$$

Subtract 1 from -3.

$$-3x^{-4}$$