Question

Choose the correct simplification of (3xy6)2(y3)3.

9x2y21
6x2y21
9x2y14
6x2y14

Answer 1

is this what you mean: \[(3xy^6)^2(y^3)^3\]?

Answer 2

9x^2y^21
6x^2y^21
9x^2y^14
6x^2y^14

Answer 3

Yes. Sorry 1 just copy and pasted it.

Answer 4

apply this rule first:
\[(a^r x^sy^t)^z=a^{r \cdot z}x^{s \cdot z}y^{t \cdot z}\]

Answer 5

\[(3^1 x^1y^6)^2=? \\ (y^3)^3=?\]

Answer 6

this rule says you are going to multiply the exponents inside by the outer exponent

Answer 7

\[3x^2y^{12} \] and\[y^9\]

Answer 8

well you just forgot to do it to 1st power on the 3

Answer 9

1 thought 3 stayed the same?

Answer 10

\[(3^1 x^1y^6)^2=3^{1 \cdot 2}x^{1 \cdot 2}y^{6 \cdot 2 }=3^{2}x^{2}y^{12} \\ (y^3)^3=y^{3 \cdot 3}=y^{9} \\ \text{ so now you have } 3^2 x^2 y^{12} \cdot y^9\]

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why would 3 stay the same when it is being squared?

Answer 11

\[3^2 \neq 3 \]

Answer 12

\[3^2=3(3)=?\]

Answer 13

okay so the first one?

Answer 14

right since \[y^{12} y^9=y^{12+9}=y^{21}\]

Answer 15

just so you know x and y are numbers just like 3 is a number

Answer 16

can you help with another?

Answer 17

okay

Answer 18

sure

Answer 19

Choose the correct simplification of \[\frac{ f ^{9} h ^{23} }{ f ^{3} h ^{17} }\]

Answer 20

use quotient rule for exponents here

Answer 21

\[\frac{u^{n}}{u^m}=u^{n-m}\]

Answer 22

\[\frac{f^9}{f^3} \cdot \frac{h^{23}}{h^{17}}=?\]

Answer 23

\[f ^{6}h ^{6}\]

Answer 24

yep
since 9-3=6 and 23-17=6

Answer 25

awesome thanks so much!

Answer 26

np