anonymous
  • anonymous
Evaluate each expression without using a calculator. Please show work! Tomorrow i have test on this and I get it in class, but by myself idk... 1. 36^3/2 2. 32^(-3/5) 3. (16/81)^(-3/4) Thank you!!:)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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austinL
  • austinL
Is it \[36^{\frac{3}{2}}\]
anonymous
  • anonymous
yes
austinL
  • austinL
\[x^{\frac{1}{2}}=\sqrt{x}\rightarrow x^{\frac{3}{2}}=\sqrt{x^3}\] \[36^{\frac{3}{2}} = \sqrt{36^{3}}\]

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anonymous
  • anonymous
okay I already had that step but then what I do because the number is too big :/
austinL
  • austinL
This one is a bit ridiculous to do without a calculator honestly. \[36^3 = 46,656\] \[\sqrt{46,656}=216\]
anonymous
  • anonymous
ikr! hopefully my teacher won't put these on the test... do you know the other two problems?
skullpatrol
  • skullpatrol
Look at $$\huge 36=6^2$$
DebbieG
  • DebbieG
Always root first, then exponent, when you can. Always always always. :)
DebbieG
  • DebbieG
All of these will be easier if you do the roots first, then the powers. They are all perfect nth roots of the root given.
skullpatrol
  • skullpatrol
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anonymous
  • anonymous
okay! sorry for the delay--my computer is all messed up :( I solved 1/8 for number 2, but I will have to continue my hw when I get back... still stuck on 3 cause idk what to do with the fraction :( thank for the explanation @skullpatrol I will keep it in mind tomorrow during the test!
DebbieG
  • DebbieG
Just use rules of roots and exponents for the fraction: \[\Large \sqrt[n]{\dfrac{ a }{ b }}=\frac{ \sqrt[n]{a} }{ \sqrt[n]{b}}\] and \[\Large \left( \dfrac{ a }{ b } \right)^n=\dfrac{ a^n }{ b^n }\]
DebbieG
  • DebbieG
and dont forget: \[\Large \left( \frac{ a }{ b } \right)^{-1}=\frac{ b }{ a }\]
skullpatrol
  • skullpatrol
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