Solve y(2/3)^-3=

$$y ( \frac { 2 } { 3 } ) ^ { - 3 } =$$

Differentiate w.r.t. y

$$\frac{27}{8} = 3\frac{3}{8} = 3.375$$

Steps Using Definition of a Derivative

Calculate \frac{2}{3} to the power of -3 and get \frac{27}{8}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y\times \frac{27}{8})$$

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

$$\frac{27}{8}y^{1-1}$$

Subtract 1 from 1.

$$\frac{27}{8}y^{0}$$

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

$$\frac{27}{8}\times 1$$

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

$$\frac{27}{8}$$

Evaluate

$$\frac{27y}{8}$$

Solution Steps

Calculate \frac{2}{3} to the power of -3 and get \frac{27}{8}.

$$y\times \frac{27}{8}$$