Solve (2u^2x^3)(3u^3x)^-2

$$( 2 u ^ { 2 } x ^ { 3 } ) ( 3 u ^ { 3 } x ) ^ { - 2 }$$

Evaluate

$$\frac{2x}{9u^{4}}$$

Solution Steps

Expand \left(3u^{3}x\right)^{-2}.

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

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

$$2u^{2}x^{3}\times 3^{-2}u^{-6}x^{-2}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$2u^{2}x^{3}\times \frac{1}{9}u^{-6}x^{-2}$$

Multiply 2 and \frac{1}{9} to get \frac{2}{9}.

$$\frac{2}{9}u^{2}x^{3}u^{-6}x^{-2}$$

To multiply powers of the same base, add their exponents. Add 2 and -6 to get -4.

$$\frac{2}{9}u^{-4}x^{3}x^{-2}$$

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$\frac{2}{9}u^{-4}x^{1}$$

Calculate x to the power of 1 and get x.

$$\frac{2}{9}u^{-4}x$$

Expand

$$\frac{2x}{9u^{4}}$$

Solution Steps

Expand \left(3u^{3}x\right)^{-2}.

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

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

$$2u^{2}x^{3}\times 3^{-2}u^{-6}x^{-2}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$2u^{2}x^{3}\times \frac{1}{9}u^{-6}x^{-2}$$

Multiply 2 and \frac{1}{9} to get \frac{2}{9}.

$$\frac{2}{9}u^{2}x^{3}u^{-6}x^{-2}$$

To multiply powers of the same base, add their exponents. Add 2 and -6 to get -4.

$$\frac{2}{9}u^{-4}x^{3}x^{-2}$$

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$\frac{2}{9}u^{-4}x^{1}$$

Calculate x to the power of 1 and get x.

$$\frac{2}{9}u^{-4}x$$