Question

Simplify the expression.



(3ax/a^2)^4

Answer 1

Hey book :)
Exponents are a little tricky.
When it's being applied to a group of stuff,
it has to be applied to each things individually.

Answer 2

Example:\[\large\rm \left(\frac{ab}{c}\right)^5=\frac{a^5b^5}{c^5}\]

Answer 3

Is this right?

\[\left( \frac{ 3^{4}a ^{4}x ^{4} }{ a ^{6} } \right)\]

Answer 4

@zepdrix

Answer 5

close, just notice that the denominator is \(a^2\)
thus \(\bf \left( \cfrac{3ax}{a^2}\right)^4\implies \left( \cfrac{3^1a^1x^1}{a^2}\right)^{\color{brown}{ 4}}\implies
\cfrac{3^{1\cdot {\color{brown}{ 4}}}a^{1\cdot {\color{brown}{ 4}}}x^{1\cdot {\color{brown}{ 4}}}}{a^{2\cdot {\color{brown}{ 4}}}}
\\ \quad \\
\cfrac{3^4\cancel{a^4} x^4}{\cancel{a^8}} \implies \cfrac{81x^4}{a^2}\)

Answer 6

hmmm

Answer 7

actually.... hold one sec... darn.. got one mistake there :/

Answer 8

\(\bf \cfrac{3^4\cancel{a^4} x^4}{\cancel{a^8}} \implies \cfrac{81x^4}{a^4}\)

Answer 9

another way to check it, would be \(\bf \cfrac{3^4a^4 x^4}{a^8} \implies 3^4a^4a^{{\color{red}{ -8}}}x^4\implies 3^4a^{4{\color{red}{ -8}}}x^4
\\ \quad \\
3^4a^{-4}x^4\implies 3^4\cdot \cfrac{1}{a^4}\cdot x^4\implies \cfrac{81x^4}{a^4}\)