How do you simplify $\frac{- 12 t^{- 1} u^{5} v^{- 4}}{2 t^{- 3} u v^{5}}$ $(-12t^-1 u^5 v^-4 )/(2t^-3 u v^5)$ ?

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Answer 1 · 2018-04-07T00:27:02

Simplified: $- \frac{6 t^{2} u^{4}}{v^{9}}$ $-(6t^2u^4)/v^9$

Expression: $\frac{- 12 t^{- 1} u^{5} v^{- 4}}{2 t^{- 3} u v^{5}}$ $(-12t^-1u^5v^-4)/(2t^-3uv^5)$

Apply fraction rule $\frac{- a}{b} = - \frac{a}{b}$ $(-a)/b = -a/b$

$= - \frac{12 t^{- 1} u^{5} v^{- 4}}{2 t^{- 3} u v^{5}}$ $=-(12t^-1u^5v^-4)/(2t^-3uv^5)$

**Divide the numbers $\frac{12}{2} = 6$ $12/2 = 6$ **

$= - \frac{6 t^{- 1} u^{5} v^{- 4}}{t^{- 3} u v^{5}}$ $=-(6t^-1u^5v^-4)/(t^-3uv^5)$

**Apply exponent rule: $\frac{x^{a}}{x^{b}} = x^{a - b}$ $x^a/x^b = x^(a-b)$ **

$= - \frac{6 t^{2} u^{5} v^{- 4}}{u v^{5}}$ $=-(6t^2u^5v^-4)/(uv^5)$

Cancel the common factor "u"

$= - \frac{6 t^{2} u^{4} v^{- 4}}{v^{5}}$ $=-(6t^2u^4v^-4)/v^5$

**Apply exponent rule: $\frac{x^{a}}{x^{b}} = x (a - b)$ $x^a/x^b=x(a-b)$ and $x^{- a} = \frac{1}{x^{a}}$ $x^-a = 1/x^a$ **

Answer $= - \frac{6 t^{2} u^{4}}{v^{9}}$ $=-(6t^2u^4)/v^9$

~ Alex

How do you simplify −12t−1u5v−42t−3uv5(-12t^-1 u^5 v^-4 )/(2t^-3 u v^5)?