How do you multiply $t^{- 1} u^{- 1} \cdot t u^{- 5} \cdot t^{- 4} u^{0}$ $t^ { - 1} u ^ { - 1} \cdot t u ^ { - 5} \cdot t ^ { - 4} u ^ { 0}$ ?

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How do you multiply $t^{- 1} u^{- 1} \cdot t u^{- 5} \cdot t^{- 4} u^{0}$ $t^ { - 1} u ^ { - 1} \cdot t u ^ { - 5} \cdot t ^ { - 4} u ^ { 0}$ ?

2 Answers

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Answer 1 · 2017-07-25T07:48:20

$= \frac{1}{t^{4} u^{6}}$ $=1/(t^4u^6)$

Explanation:

Recall two of the laws of indices.

$x^{- m} = \frac{1}{x^{m}} and \frac{1}{x^{- n}} = x^{n}$ $x^-m = 1/x^m" and " 1/x^-n = x^n$

$x^{0} = 1 (0^{0}$ $x^0 = 1" "(0^0$ is undefined)

$t^{- 1} u^{- 1} \times t u^{- 5} \times t^{- 4} u^{0}$ $color(red)(t^-1u^-1) xx tcolor(blue)(u^-5) xx color(green)(t^-4)color(magenta)(u^0)$

$= \frac{1}{t u} \times \frac{t}{u^{5}} \times \frac{1}{t^{4}} \times 1 \leftarrow$ $= 1/(color(red)(tu)) xx t/color(blue)(u^5) xx 1/color(green)(t^4) xx color(magenta)(1)" "larr$ all positive indices

$= 1/(canceltu) xx cancelt/u^5 xx 1/t^4$

$=1/(t^4u^6)$

Answer 2 · 2017-07-25T07:49:27

$t^(-1)u^(-1)*tu^(-5)*t^-4u^0=1/(t^4u^6$

Explanation:

$t^(-1)u^(-1)*tu^(-5)*t^-4u^0$

= $(t^(-1)*t^1*t^-4)*(u^(-1)*u^(-5)*u^0)$

= $t^(-1+1+(-4))*u^(-1+(-5)+0)$

= $t^(-4)*u^(-6)$

= $1/(t^4u^6$

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How do you multiply $t^{- 1} u^{- 1} \cdot t u^{- 5} \cdot t^{- 4} u^{0}$ $t^ { - 1} u ^ { - 1} \cdot t u ^ { - 5} \cdot t ^ { - 4} u ^ { 0}$ ?

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How do you multiply $t^{- 1} u^{- 1} \cdot t u^{- 5} \cdot t^{- 4} u^{0}$ $t^ { - 1} u ^ { - 1} \cdot t u ^ { - 5} \cdot t ^ { - 4} u ^ { 0}$ ?