What is factor (3u^{-3}v^{-2})^{-2} ?

The solution to factor (3u^{-3}v^{-2})^{-2} is (u^6v^4)/9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor (3u^{-3}v^{-2})^{-2}

factor

(3 u^{- 3} v^{- 2})^{- 2}

\frac{u ^{6} v ^{4}}{9}

Solution steps

(3 u^{- 3} v^{- 2})^{- 2}

Multiply

3 u^{- 3} v^{- 2} : \frac{3}{u ^{3} v ^{2}}

= (\frac{3}{u ^{3} v ^{2}})^{- 2}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{( \frac{3}{u ^{3} v ^{2}} ) ^{2}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{3}{u ^{3} v ^{2}})^{2} = \frac{3 ^{2}}{( u ^{3} v ^{2} ) ^{2}}

= \frac{1}{\frac{3 ^{2}}{( u ^{3} v ^{2} ) ^{2}}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(u^{3} v^{2})^{2} = (u^{3})^{2} (v^{2})^{2}

= \frac{1}{\frac{3 ^{2}}{( u ^{3} ) ^{2} ( v ^{2} ) ^{2}}}

(u^{3})^{2} : u^{6}

= \frac{1}{\frac{3 ^{2}}{u ^{6} ( v ^{2} ) ^{2}}}

(v^{2})^{2} : v^{4}

= \frac{1}{\frac{3 ^{2}}{u ^{6} v ^{4}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{u ^{6} v ^{4}}{3 ^{2}}

3^{2} = 9

= \frac{u ^{6} v ^{4}}{9}

x^{- 1} + 2 + x

(6 x - 5)^{3} - 8

(b)^{3}

x^{15} y^{12} z^{6} - 343

10 am + 2 bm + bn + 5 an

What is factor (3u^{-3}v^{-2})^{-2} ?
The solution to factor (3u^{-3}v^{-2})^{-2} is (u^6v^4)/9