Question

Simplify (3x^3y^4)^2/(6x^5y^3)(x^3y^2)^4

1/x^7y^3
3/2x^11y^3
3x^11y^3/2
9x^6/y^3

Answer 1

familiar with the exponent rules ?

Answer 2

Not much :/

Answer 3

alright
exponent rules \[\huge\rm (ab)^m =a^mb^m\]
numbers/variables in the parentheses raised by m power
when we multiply same bases we should `add` exponents \[\huge\rm x^m \times x^n=x^{m+n}\]
and when we divide same base , `subtract` their exponents \[\huge\rm \frac{ x^m }{ x^n }=x^{m-n}\]

Answer 4

\[\huge\rm \frac{ \color{ReD}{(3x^3y^4)^2}}{(6x^5y^3)(x^3y^2)^4}\]
start with first exponent rule i posted above

Answer 5

\[\huge\rm {(3x^3y^4)^2} = ??\]

Answer 6

Would it be (3x^5y^6)?

Answer 7

I'm not good at math :/

Answer 8

multiply the exponents

Answer 9

you will be one day

Answer 10

exponent rules \[\huge\rm (a^1b^1)^m =a^{1 \times m}b^{1 \times m}\]
numbers/variables in the parentheses raised by m power
according to this rule \[\huge\rm {(3x^3y^4)^2} = 3^3 x^{3 \times2}y^{4 \times3}\]
every number/variable in the parentheses raised by 2 power
multiply the exponents

Answer 11

3^3x^6y^12

Answer 12

sorry there is a typo
\[\huge\rm {(3x^3y^4)^2} = 3^2 x^{3 \times2}y^{4 \times3}\]

3 to the 2 power not 3

Answer 13

Ok

Answer 14

the power tells us how many times we should multiply the base
3^2 = 3 times 3

Answer 15

Ok

Answer 16

ugh typo sorry there is a typo
\[\huge\rm {(3x^3y^4)^2} = 3^2 x^{3 \times2}y^{4 \times2}\]

3 to the 2 power not 3
and y^4 times 2 not 3
now simplify that

Answer 17

\[(3x ^{3}y ^{4})^{2} = 3^{2}x ^{6}y ^{8}\]

Answer 18

yes right what about 3^2 = ?

Answer 19

9

Answer 20

yes right so \[\huge\rm \frac{ \color{ReD}{9x^6y^8}}{(6x^5y^3)(x^3y^2)^4}\]
now apply the same exponent rule for (x^3y^2)^4

Answer 21

Would i combine them?

Answer 22

apply the exponent rule just like we did for the numerator

Answer 23

Because I got \[x ^{12}y ^{8}\]

Answer 24

would I multiply the 4 to the other one too?

Answer 25

no bec 4 is power of x^3 y^2 so that's it for this part \[\huge\rm \frac{ \color{black}{9x^6y^8}}{(6x^5y^3)x^{12}y^{8}}\]

you can remove the parentheses from (6x^5y^3) bec there isn't any exponent outside the parentheses



\[\huge\rm \frac{ \color{black}{9x^6y^8}}{6x^5y^3x^{12}y^{8}}\]

now apply the 2nd exponent rule

~when we multiply same bases we should `add` exponents \[\huge\rm x^m \times x^n=x^{m+n}\]

Answer 26

\[6x ^{17}y ^{11}\]

Answer 27

nice
\[\huge\rm \frac{ \color{black}{9x^6y^8}}{6x^{17}y^{11}}\]


reduce the fraction 9/6 and apply the exponent rule when we divide same base , `subtract` their exponents \[\huge\rm \frac{ x^m }{ x^n }=x^{m-n}\]

Answer 28

3x^11y^3/2

Answer 29

hmm
top exponent `minus` bottom exxponents
so `6-17` = ?

Answer 30

oh -11 and -3

Answer 31

yes right now we need to change negative to positive exponent
\[\huge\rm x^{-m}=\frac{ 1 }{ x^m }\]
to convert negative to positive exponent u should flip the fraction , when you flip it the sign of the exponent would change

Answer 32

So 3/2x^11y^3

Answer 33

looks good

Answer 34

Thank you so much!

Answer 35

np good work
you just need to practice more on this stuff then you will be an expert at exponent rules

Answer 36

I will keep practicing, thank you again.

Answer 37

o^_^o