where am I wrong ?

The question is to simplify the espression[attachment=0:eek:gsb835d]2.JPG[/attachment:eek:gsb835d]

The answer is 27
 
Going from the second to the third line I think you multiplied the second exponent by 3 instead of 2.
 
DanieldeLucena said:
The question is to simplify the espression[attachment=0:23zfwofp]2.JPG[/attachment:23zfwofp]

The answer is 27
Click to expand...


I sure hope that someone will be able to explain how that becomes 27.....

[(3[sup:23zfwofp]12[/sup:23zfwofp] + 9[sup:23zfwofp]2[/sup:23zfwofp])/30][sup:23zfwofp](1/5)[/sup:23zfwofp]

9 is 3[sup:23zfwofp]2[/sup:23zfwofp], so 9[sup:23zfwofp]2[/sup:23zfwofp] can be written as (3[sup:23zfwofp]2[/sup:23zfwofp])[sup:23zfwofp]2[/sup:23zfwofp], or 3[sup:23zfwofp]4[/sup:23zfwofp].....

So, now we have

[(3[sup:23zfwofp]12[/sup:23zfwofp] + 3[sup:23zfwofp]4[/sup:23zfwofp]) / 30 ][sup:23zfwofp](1/5)[/sup:23zfwofp]

30 is 3*10....and we can factor 3[sup:23zfwofp]4[/sup:23zfwofp] out of both terms of the numerator:

[3[sup:23zfwofp]4[/sup:23zfwofp](3[sup:23zfwofp]8[/sup:23zfwofp] + 1) / (3*10)][sup:23zfwofp](1/5)[/sup:23zfwofp]

Reduce the fraction by dividing a factor of 3 out of both numerator and denominator:

[3[sup:23zfwofp]3[/sup:23zfwofp](3[sup:23zfwofp]8[/sup:23zfwofp] + 1) / 10][sup:23zfwofp](1/5)[/sup:23zfwofp]

I don't know...I'm not getting anything CLOSE to 27 out of this. Did I mis-interpret something in the original problem?
 
\(\displaystyle \left[\frac{3^{18}+9^8}{30}\right ]^{\frac{1}{5}}\)

\(\displaystyle = \ \left[\frac{3^{18}+3^{16}}{30}\right ]^{\frac{1}{5}}\)

\(\displaystyle = \ \left[\frac{3^{16}(3^2+1)}{30}\right ]^{\frac{1}{5}}\)

\(\displaystyle = \ \left[\frac{3^{16}}{3}\right ]^{\frac{1}{5}}\)

\(\displaystyle = \ \left[3^{15}\right ]^{\frac{1}{5}}\)

\(\displaystyle = \ 3^3 \ = \ 27\)
 
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