Question

Evaluate as a fraction or an integer: (3^6) (3^-3)


-27

27

-1/27

1/27

Answer 1

\[\huge\color{blue}{ a^{-b}=\frac{1}{a^b} }\]this way,\[\huge\color{blue}{ 3^{-3}=\frac{1}{3^3}=\frac{1}{27} }\]

Answer 2

Fred pays 2/5 of his annual salary in federal, state, and local taxes. His annual salary is 102,000. How much of his salary does he get to keep after taxes are paid?


$61,000

$72,300

$61,200

$94,900

Answer 3

So, (for your first problem)\[\color{blue}{ 3^6 \times 3^{-3}~~~~~~is~~same~~~as,~~~~~3^6 \times\frac{1}{27} ~~~which~~is~~same~~as, }\]\[-->~~~\frac{3^6}{27}\]

Answer 4

ya i get the first one now.

Answer 5

\[\color{red}{ \frac{3^6}{3^3} ~~~->~~~3^6 \div 3^3~~~->~~~3^{(6-3)}~~~->~~~3^3~~~->~~~27. }\]

Answer 6

The anwer is 27 right?

Answer 7

Could you help me on the second problem?

Answer 8

YES.

Problem 2:

@cliche, If he pays 2/5 of his salary he gets to keep 3/5 correct?

Answer 9

yes

Answer 10

We know that his ENTIRE SALARY is 102,000. if he pays 2/5, he keeps 3/5 because the entire salary is 5/5 (five fifths).

So what is 3/5 of 100,200?
\[\huge\color{red}{ 102,000 \times \frac{3}{5} =~~~you~~~tell~~me. }\]

Answer 11

x^m *x^-n=x^(m-n)

Answer 12

yeah, I was just showing how that works.

Answer 13

\[\huge\color{black}{ D \times \frac{s}{v}=D \times s \div v } \]

Answer 14

im confused i tried it and cam out with this 2871044762448589/46912496118441

Answer 15

@SolomonZelman