Solve 1/3^-3y^-2=

$$\frac { 1 } { 3 ^ { - 3 } } y ^ { - 2 } =$$

Evaluate

$$\frac{27}{y^{2}}$$

Solution Steps

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{1}{\frac{1}{27}}y^{-2}$$

Divide 1 by \frac{1}{27} by multiplying 1 by the reciprocal of \frac{1}{27}.

$$1\times 27y^{-2}$$

Multiply 1 and 27 to get 27.

$$27y^{-2}$$

Differentiate w.r.t. y

$$-\frac{54}{y^{3}}$$

Steps Using Definition of a Derivative

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{\frac{1}{27}}y^{-2})$$

Divide 1 by \frac{1}{27} by multiplying 1 by the reciprocal of \frac{1}{27}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(1\times 27y^{-2})$$

Multiply 1 and 27 to get 27.

$$\frac{\mathrm{d}}{\mathrm{d}y}(27y^{-2})$$

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

$$-2\times 27y^{-2-1}$$

Multiply -2 times 27.

$$-54y^{-2-1}$$

Subtract 1 from -2.

$$-54y^{-3}$$