Helpp ?

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#1. Peter did not simplify his answer completely because he did not reach the conclusion of \[x ^{12}\] second part of the problem is that \[x^3 x^3 x^3 x^3 \neq x^3 + x^3 + x^3 + x^3\] so Peter's work would NOT be the same.
\[x^3 + x^3 + x^3 + x^3 = 4x^3\]

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#2. use property of negative exponents in addition to fractional exponents. #3. use quotient property since the base is the same.
#4.\[\sqrt[3]{x^3} = x ^{3*(1/3)}\] involves powers of a product \[x ^{1/3}x ^{1/3}x ^{1/3} = x ^{(1/3) + (1/3) + (1/3)} = x ^{3/3} = x\] involves product of powers \[1/x ^{-1} = x ^{1} = x\] involves negative exponents
Could you help me on showing my work for #2 and #3 ? I don't even know where to begin ..
\[\sqrt[n]{x}=\left( x \right)^{\frac{ 1 }{n }}\]
\[\frac{ 1 }{\sqrt[3]{x ^{-6}} }=\frac{ 1 }{\left( x ^{-6} \right)^{\frac{ 1 }{3 }} }=\frac{ 1 }{\left( x \right)^{-6*\frac{ 1 }{ 3 }} } =\frac{ 1 }{ x ^{-2 } } =x ^{2}\] i think i have cleared everything,if any doubt ask me.
I'm starting to understand
Would number 3 be |dw:1378942627571:dw| ??
\[\frac{ x ^{\frac{ 2 }{ 3 }} }{ x ^{\frac{ 4 }{9 }} }=x ^{\frac{ 2 }{3 }}*x ^{\frac{ -4 }{9 }}\] \[=x ^{\left( \frac{ 2 }{ 3 }-\frac{ 4 }{9 } \right)}\] take L.C.M and solve.
L C M ?
when bases are same powers are added during multiplication.
Ohh okay
Okay no I don't get it ..... None of this makes sense :( What's being added and what's being multiplied here ?
\[x ^{a}*x ^{b}=x ^{a+b}\]
for #3, when you have the same bases, and it is a division problem, the powers are subtracted. the power from the denominator is subtracted from the power in the numerator like so \[x ^{2/3}/x ^{4/9} = x ^{(2/3)-(4/9)}\]
\[\frac{ 2 }{3 }and \frac{ -4 }{ 9 } are added\]
I would be able to figure that out if I could find my freaking scientific calculator :'c
\[\frac{ 2 }{3 }and \frac{ -4 }{ 9 } are added\]
2/9 ?
\[yes x ^{\frac{ 2 }{ 9 }}\]
use this property when you see a problem like #3 \[x ^{m}/x ^{n} = x ^{m-n}\]
Okay
So is 2/9 the answer then ? :o
yep
Okay thank you so much
note that answer is not 2/9 it is as i have given above x ^2/9
Ohh okay well that makes more sense now . Thank YOU
yw

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