Question

Which is the simplified form of 15 times q times r to the fifth power all over 3 times q cubed times r to the fourth power.?

5 times r all over q squared.
12 times r all over q squared.
5 times q squared all over r.
12 times q squared all over r.

Answer 1

so the problem is

\[\large \frac{15qr^{5}}{3qr^{4}}\]

right?

Answer 2

thats very close but on the denomenator there is a power of 3 on the q but other whys it's perfect.

Answer 3

oh my bad

Answer 4

so

\[\large \frac{15qr^{5}}{3q^{3}r^{4}}\]

??

Answer 5

yes sir,

Answer 6

ok thx, one sec

Answer 7

My problem is i know how to simplify the 15 and 3 but i don't know how to simplify the exponents.

Answer 8

Here's how you simplify


\[\large \frac{15qr^{5}}{3q^{3}r^{4}}\]


\[\large \frac{15}{3}*\frac{q}{q^{3}}*\frac{r^{5}}{r^{4}}\]


\[\large \frac{5}{1}*\frac{q^{1-3}}{1}*\frac{r^{5-4}}{1}\]


\[\large \frac{5}{1}*\frac{q^{-2}}{1}*\frac{r^1}{1}\]


\[\large \frac{5}{1}*\frac{1}{q^{2}}*\frac{r}{1}\]


\[\large \frac{5*1*r}{1*q^{2}*1}\]


\[\large \frac{5r}{q^{2}}\]

Answer 9

when dividing exponential terms, you subtract the exponents

Answer 10

so for instance

x^7 divided by x^3 = x^(7-3) = x^4

Answer 11

ok so thats how Q^3 became q

Answer 12

what do you mean?

Answer 13

well like you said you subtract the exponents when, your dividing so would you divide the bottom exponents but the alike exponents on the top.
which is actullay my bad because the q^3 - q^1 = q^2?

Answer 14

yes it's the other way around actually

q divided by q^3

q^1 divided by q^3

q^(1-3)

q^(-2)

1/( q^2 )

Answer 15

I'm using the idea that

x^( -k ) = 1/( x^k )

Answer 16

what does the 1/ in front mean?

Answer 17

1 over

Answer 18

1/x means \(\large \frac{1}{x}\)

Answer 19

so instead of saying "2 over 3", you would say 2/3

Answer 20

oh wait is it like how you have a negative in a equation and you have to, take the negative out with a positive?

Answer 21

kind of...

Answer 22

the negative exponent is made positive by flipping the fraction

Answer 23

oh ok, sorry if im being a little oblivious.

Answer 24

no its ok, it's good you're asking

Answer 25

well thankyou sir,

Answer 26

you're welcome

Answer 27

Im gonna go practice this on some other questions, if i have any difficulties I will just post another question, but again thank you for your help.

Answer 28

sure thing, and good idea, practice makes perfect