Mathematics
8 Online
OpenStudy (anonymous):
exponent question
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OpenStudy (amistre64):
what part of it do you ahve questions about?
OpenStudy (anonymous):
with the first one, \[\frac{ 3xy ^{2}(xy)^{1} }{ z ^{4} }\]\[\frac{ 3x ^{2}y ^{3} }{ z ^{4} }\]
OpenStudy (anonymous):
just want to make sure im doing these right
OpenStudy (amistre64):
its good so far
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OpenStudy (anonymous):
isnt that as far are you can simplify
OpenStudy (amistre64):
yep
OpenStudy (anonymous):
\[(3m^2)^3(2mn)^{-1}(8n^3)^\frac{ 2 }{ 3 }\]
OpenStudy (anonymous):
so you'd have \[(3m^6)(\frac{ 1 }{ 2mn})\]
OpenStudy (anonymous):
but what do you do with the 8n stuff?
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OpenStudy (amistre64):
you missed something
OpenStudy (anonymous):
what? the last group?
OpenStudy (amistre64):
a^3 = a*a*a
but a = 3mm
3mm*3mm*3mm = 3^3 m^6 not 3m^6
OpenStudy (anonymous):
so 27m^6
OpenStudy (amistre64):
yes
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OpenStudy (anonymous):
\[\sqrt[3]{8n^3}^2\]
OpenStudy (anonymous):
would that be the last group?
OpenStudy (amistre64):
\[b^{m/n} =(b^m)^{1/n}=\sqrt[n]{~b^m~}\]
OpenStudy (anonymous):
\[(3m^6)(\frac{ 1 }{ 2mn })(\sqrt[3]{8n^3})^2\]
OpenStudy (amistre64):
cuberoot is good
cbrt(8.8.nnn.nnn) = 2.2.n.n
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OpenStudy (amistre64):
does tha tmake any sense?
OpenStudy (amistre64):
\[(3^3m^6)(\frac{ 1 }{ 2mn })\sqrt[3]{(8n^3)^2~}\]
OpenStudy (amistre64):
3.3.3.m.m.m.m.m.m.1.2.2.n.n
--------------------------
2.m.n
3.3.3.m.m.m.m.m.2.n
OpenStudy (anonymous):
\[\sqrt[3]{8n^3}^2 \sqrt[3]{64^6} 4n^2\]
OpenStudy (anonymous):
so \[(27m^6)(\frac{ 1 }{ 2mn })(4n^2)\]
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OpenStudy (amistre64):
yep
OpenStudy (anonymous):
any way to simplify that or is that it?
OpenStudy (amistre64):
well, if we simplify it to the max ....
3.3.3.m.m.m.m.m.m.1.2.2.n.n
--------------------------
2.m.n
3.3.3.m.m.m.m.m.2.n
OpenStudy (amistre64):
a 2,m,n cancel with a 2,m,n on top
OpenStudy (anonymous):
\[27m^52n\]
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OpenStudy (amistre64):
almost there, 27*2 is?
OpenStudy (anonymous):
54
OpenStudy (amistre64):
good
OpenStudy (anonymous):
\[54m^5n\]
OpenStudy (amistre64):
\[(3m^2)^3(2mn)^{-1}(8n^3)^\frac{ 2 }{ 3 }\]
\[27m^{2*3}~(2^{-1}m^{-1}n^{-1})~ (64n^{2*3})^\frac{ 1 }{ 3 }\]
\[27m^{6}~(2^{-1}m^{-1}n^{-1})~64^{1/3}n^{2*3/3}\]
\[27m^{6}~(2^{-1}m^{-1}n^{-1})~4n^{2}\]
\[27m^{6-1}~\frac42n^{2-1}\]
\[27(2)~m^{5}~n\]
yes
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OpenStudy (anonymous):
that was a bit of a pain. :P thanks
OpenStudy (amistre64):
ye sit was lol