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Mathematics 8 Online
OpenStudy (anonymous):

exponent question

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

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?

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

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

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 \[(27m^6)(\frac{ 1 }{ 2mn })(4n^2)\]

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):

\[27m^52n\]

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

OpenStudy (anonymous):

that was a bit of a pain. :P thanks

OpenStudy (amistre64):

ye sit was lol

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