Question

How do you evaluate the expression `(1/5)^-4/((1/5)^-2(1/5)^-5)` using the properties?

Answer 1

`1/125`

Explanation:

Set `x=1/5` to make things clearer

`x^(-4)/(x^(-2)x^(-5))`

`=x^(-4)/x^(-7)`

Note that `1/x^(-7)` is the same as `x^7`

Note that `x^(-4)` is the same as `1/x^4`

Putting it all together we have:

`x^7/x^4`
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Method 1: `->x^(7-4)=x^3`

Method 2: `->1/(cancel(x^4))xx cancel(x^4)xxx^3" "=" "x^3`

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Finally, replace `x` with `1/5` and simplify.

`x^3 = (1/5)^3 = 1^3/5^3 = 1/125`

Final Answer