Question

simplify the expression.
14ab^3
--------
7a^-2b^-1

Answer 1

Do you know the rules for negative exponents?

Answer 2

no.

Answer 3

\[\frac{1}{x^{-1}}=x\text{ and }x^{-1}=\frac{1}{x}\]

Answer 4

So on yours:\[\frac{14ab^3}{7a^{-2}b^{-1}}\]Do you see how the negative exponents will become positive if they are moved to the top?

Answer 5

oh yes! because of the negative exponent, i get what you're saying now.

Answer 6

would you mind explaining it step by step?

Answer 7

When they are on the top, then you do combined like terms. The only other thing to do would be to simplify the 14 over 7 part.

Answer 8

so would it be \[2a ^{-2}b ^{-3}\] ?

Answer 9

Not quite... The 2 is great! But you did not do the exponents correctly.

Answer 10

\[2a ^{3}b ^{4}\] ?

Answer 11

Yes!

Answer 12

That is the right way to do it!

Answer 13

thank you!

Answer 14

So just to review it:\[\frac{14ab^3}{7a^{-2}b^{-1}}\implies\\ \, \\
\frac{2ab^3}{a^{-2}b^{-1}}\implies \\ \, \\
\frac{2aa^2b^3b}{1}\implies\\\, \\
2a^3b^4\]

Answer 15

thank you so much, i really appreciate it! (:

Answer 16

NP. have fun!