Solve 3^-3*u^-2*v*54u^3v

$$3 ^ { - 3 } \cdot u ^ { - 2 } \cdot v \cdot 54 u ^ { 3 } v$$

Evaluate

$$2uv^{2}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$3^{-3}u^{-2}v^{1}\times 54^{1}u^{3}v^{1}$$

Use the Commutative Property of Multiplication.

$$3^{-3}\times 54^{1}u^{-2}u^{3}v^{1}v^{1}$$

To multiply powers of the same base, add their exponents.

$$3^{-3}\times 54^{1}u^{-2+3}v^{1+1}$$

Add the exponents -2 and 3.

$$3^{-3}\times 54^{1}u^{1}v^{1+1}$$

Add the exponents 1 and 1.

$$3^{-3}\times 54^{1}uv^{2}$$

Raise 3 to the power -3.

$$\frac{1}{27}\times 54^{1}uv^{2}$$

Multiply \frac{1}{27} times 54.

$$2uv^{2}$$

Differentiate w.r.t. u

$$2v^{2}$$