Question 6305
<font face = "courier new" size = 3><b>simplify:
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<font face = "symbol">Ö</font>81c<sup>5</sup>d<sup>4</sup>
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Prime factor 81 = 9·9 = 3·3·3·3
Prime factor c<sup>5</sup> = c·c·c·c·c
Prime factor d<sup>4</sup> = d·d·d·d
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<font face = "symbol">Ö</font>81c<sup>5</sup>d<sup>4</sup> =
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<font face = "symbol">Ö</font>3·3·3·3·c·c·c·c·c·d·d·d·d =
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<font face = "symbol">Ö</font>(3·3)·(3·3)·(c·c)·(c·c)·c·(d·d)·(d·d) =
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<font face = "symbol">Ö</font>(3<sup>2</sup>)·(3<sup>2</sup>)·(c<sup>2</sup>)·(c<sup>2</sup>)·c·(d<sup>2</sup>)·(d<sup>2</sup>) =
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<font face = "symbol">Ö</font>3<sup>2</sup>·<font face = "symbol">Ö</font>3<sup>2</sup>·<font face = "symbol">Ö</font>c<sup>2</sup>·<font face = "symbol">Ö</font>c<sup>2</sup>·<font face = "symbol">Ö</font>c·<font face = "symbol">Ö</font>d<sup>2</sup>·<font face = "symbol">Ö</font>d<sup>2</sup> =
` ` ` ` ` ` ` ` `_
`3 · 3 · c · c ·<font face = "symbol">Ö</font>c· d · d =
` ` ``_
9·c<sup>2</sup>·<font face = "symbol">Ö</font>c·d<sup>2</sup>
` ` ` _
9c<sup>2</sup>d<sup>2</sup><font face = "symbol">Ö</font>c
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Edwin