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(3^2n times a^3)^2 = ?

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hmm does it have choices? my answer is 9a^6n but i could be wrong
\[(3^{4n}a ^{3})^{2^{}} = ???\]
ok sorry i was wrong

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Other answers:

@TjRoDz you're wrong...
uhh 81a^6n
still wrong @TjRoDz
hhhaha my pea sized brain
help me please @thomaster
uhm i think \(\sf\Large a^6\large3^{\Large8n}\)
\(\Large (a^n)^m=a^{n*m}\)
wont it be instead of 3 it would be squared and be 9?
@thomaster wont it be: instead of 3; it would be squared and be 9?
i'm confused
No \(\Large(3^{4n}a ^3)^2\) 4*2=8 and 3*2=6 \(\Large3^{8n}a ^6~\to~a^63^{8n}\)
  • phi
you can memorize the rule \[ (x^a)^b = x^{ab} \] which means multiply the exponents but you can use this idea: \[ x^2 \text{ means } x \cdot x \] so \[ (3^{4n}a ^{3})^{2} \text{ means } (3^{4n}a ^{3})(3^{4n}a ^{3}) \]
  • phi
you can re-arrange that to \[ (3^{4n}\cdot 3^{4n}\cdot a ^{3}\cdot a ^{3})\]
  • phi
if you don't know about "adding exponents" you could figure out \[ a^3 \cdot a^3 \] by knowing that \(a^3 = a\cdot a \cdot a \) \[ a^3 \cdot a^3 = a\cdot a \cdot a \cdot a\cdot a \cdot a= a^6\]
  • phi
but to do \[ 3^{4n} \cdot 3^{4n} \] you need to know the rule: if you have the same base, add the exponents \[ 3^{4n+4n} \] or \[3^{8n} \]

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