Simplify $\text{}\frac{(0.81{)}^{2}\times (0.6\times 0.21{)}^{2}}{{35}^{5}\times 0.252}$ into ${2}^{n}\times {3}^{m}\times {5}^{p}\times {7}^{k}$ where n,m,p,k are integers.

Marcus Bass
2022-09-20
Answered

Simplify $\text{}\frac{(0.81{)}^{2}\times (0.6\times 0.21{)}^{2}}{{35}^{5}\times 0.252}$ into ${2}^{n}\times {3}^{m}\times {5}^{p}\times {7}^{k}$ where n,m,p,k are integers.

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Negative Indices

I am not exactly good at evaluating negative indices--can someone please show me how to work out this expression:

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Thanks!

I am not exactly good at evaluating negative indices--can someone please show me how to work out this expression:

$\frac{{m}^{-3}{n}^{-2}}{{m}^{-5}{n}^{6}}$

Both m's and the top n have negative indices.

Thanks!

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$\sqrt{{n}^{2}+n}-n=\frac{({n}^{2}+n)-{n}^{2}}{\sqrt{{n}^{2}+n}+n}$

I was trying to make sense of it, but I didnt succeed.

Can you give me a hint or tell me how this tranformation is called ?

I was looking through my notes when I stumbled upon this eqation:

$\sqrt{{n}^{2}+n}-n=\frac{({n}^{2}+n)-{n}^{2}}{\sqrt{{n}^{2}+n}+n}$

I was trying to make sense of it, but I didnt succeed.

Can you give me a hint or tell me how this tranformation is called ?

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How do I do this derivation step? I don't understand why there is equality. The derivation is from my textbook.

$mg-m\left(\frac{g}{1+\frac{M}{2m}}\right)=\frac{mg}{1+\frac{2m}{M}}$