Question

How would i answer this? Link Below.

Answer 1

\[\Huge \frac{1}{x^{{}^{\frac{-3}{6}}}}\]

Answer 2

First reduce -3/6 to get -1/2

\[\Huge \frac{1}{x^{{}^{\frac{-3}{6}}}}=\frac{1}{x^{{}^{-\frac{1}{2}}}}\]

Answer 3

Then use the rule
\[\LARGE \frac{1}{x^{-k}} = x^k\]
to get
\[\Huge \frac{1}{x^{{}^{\frac{-1}{2}}}} = x^{{}^{\frac{1}{2}}}\]
are you with me so far?

Answer 4

@jim_thompson5910 if I'm being honest with you, I'm totally lost. All of the signs are really confusing:(

Answer 5

do you see how I reduced -3/6 to get -1/2 ??

Answer 6

oh okay, i understand that... sorry @jim_thompson5910

Answer 7

that's ok

Answer 8

have you seen this rule at all before?

\[\LARGE \frac{1}{x^{-k}} = x^k\]

Answer 9

no:/

Answer 10

Basically negative exponents mean we take the reciprocal of the base to get the exponent to be positive


Examples:
\[\LARGE \frac{1}{x^{-2}} = x^2\]
\[\LARGE x^{-3} = \frac{1}{x^{3}}\]

notice how the x flips to 1/x or vice versa

Answer 11

here is another page that has a lesson on negative exponents if you want more practice

http://www.purplemath.com/modules/exponent2.htm

Answer 12

so then you would have

Answer 13

after reducing the -3/6 to -1/2, yes

Answer 14

now we can take the reciprocal of the 1/x to get x/1 which is just x

taking the reciprocal changes the negative 1/2 into positive 1/2