Solve [[(-3)^2]^3]x(-3)^2

$$[ [ ( - 3 ) ^ { 2 } ] ^ { 3 } ] x ( - 3 ) ^ { 2 }$$

Evaluate

$$6561x$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(-3\right)^{6}x\left(-3\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\left(-3\right)^{8}x$$

Calculate -3 to the power of 8 and get 6561.

$$6561x$$

Differentiate w.r.t. x

$$6561$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-3\right)^{6}x\left(-3\right)^{2})$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-3\right)^{8}x)$$

Calculate -3 to the power of 8 and get 6561.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6561x)$$

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

$$6561x^{1-1}$$

Subtract 1 from 1.

$$6561x^{0}$$

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

$$6561\times 1$$

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

$$6561$$