Mammoth Memory

Indices and double negatives

Simplify  `(x^-4)^-2`

To tackle this problem try simple numbers you know first.

We know

`10^-2=1/10^2=1/(10\times10)=1/100=0.01`
 

Therefore  `x^(-4)=1/(x^4)`

And therefore  `(x^-4)^-2=(1/x^4)^-2`

Which equals  `1/((1/(x^4))^2`  

And  `1/{1/x^4\times1/x^4`              

And as  `1/2\times1/2=1/4` 

Then `1/{1/x^4\times1/x^4\}=1/{1/x^16}` 

 

`x^16/1` 

We get  `x^16`    

Answer:

`(x^-4)^-2=\x^16` 

This makes sense because two negatives make a positive, but it’s excellent to check.

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