Solve (-3)^3x(-3)^4/(-3)^5

$$\frac { ( - 3 ) ^ { 3 } x ( - 3 ) ^ { 4 } } { ( - 3 ) ^ { 5 } }$$

Evaluate

$$9x$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\left(-3\right)^{7}x}{\left(-3\right)^{5}}$$

Cancel out \left(-3\right)^{5} in both numerator and denominator.

$$\left(-3\right)^{2}x$$

Calculate -3 to the power of 2 and get 9.

$$9x$$

Differentiate w.r.t. x

$$9$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(-3\right)^{7}x}{\left(-3\right)^{5}})$$

Cancel out \left(-3\right)^{5} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-3\right)^{2}x)$$

Calculate -3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x)$$

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

$$9x^{1-1}$$

Subtract 1 from 1.

$$9x^{0}$$

For any term t except 0, t^{0}=1.

$$9\times 1$$

For any term t, t\times 1=t and 1t=t.

$$9$$