## LaynaMae 2 years ago Helpp ?

1. LaynaMae

2. djaydeej88

#1. Peter did not simplify his answer completely because he did not reach the conclusion of $x ^{12}$ second part of the problem is that $x^3 x^3 x^3 x^3 \neq x^3 + x^3 + x^3 + x^3$ so Peter's work would NOT be the same.

3. djaydeej88

$x^3 + x^3 + x^3 + x^3 = 4x^3$

4. djaydeej88

#2. use property of negative exponents in addition to fractional exponents. #3. use quotient property since the base is the same.

5. djaydeej88

#4.$\sqrt[3]{x^3} = x ^{3*(1/3)}$ involves powers of a product $x ^{1/3}x ^{1/3}x ^{1/3} = x ^{(1/3) + (1/3) + (1/3)} = x ^{3/3} = x$ involves product of powers $1/x ^{-1} = x ^{1} = x$ involves negative exponents

6. LaynaMae

Could you help me on showing my work for #2 and #3 ? I don't even know where to begin ..

7. surjithayer

$\sqrt[n]{x}=\left( x \right)^{\frac{ 1 }{n }}$

8. surjithayer

$\frac{ 1 }{\sqrt[3]{x ^{-6}} }=\frac{ 1 }{\left( x ^{-6} \right)^{\frac{ 1 }{3 }} }=\frac{ 1 }{\left( x \right)^{-6*\frac{ 1 }{ 3 }} } =\frac{ 1 }{ x ^{-2 } } =x ^{2}$ i think i have cleared everything,if any doubt ask me.

9. LaynaMae

I'm starting to understand

10. LaynaMae

Would number 3 be |dw:1378942627571:dw| ??

11. surjithayer

$\frac{ x ^{\frac{ 2 }{ 3 }} }{ x ^{\frac{ 4 }{9 }} }=x ^{\frac{ 2 }{3 }}*x ^{\frac{ -4 }{9 }}$ $=x ^{\left( \frac{ 2 }{ 3 }-\frac{ 4 }{9 } \right)}$ take L.C.M and solve.

12. LaynaMae

L C M ?

13. surjithayer

when bases are same powers are added during multiplication.

14. LaynaMae

Ohh okay

15. LaynaMae

Okay no I don't get it ..... None of this makes sense :( What's being added and what's being multiplied here ?

16. surjithayer

$x ^{a}*x ^{b}=x ^{a+b}$

17. djaydeej88

for #3, when you have the same bases, and it is a division problem, the powers are subtracted. the power from the denominator is subtracted from the power in the numerator like so $x ^{2/3}/x ^{4/9} = x ^{(2/3)-(4/9)}$

18. surjithayer

$\frac{ 2 }{3 }and \frac{ -4 }{ 9 } are added$

19. LaynaMae

I would be able to figure that out if I could find my freaking scientific calculator :'c

20. surjithayer

$\frac{ 2 }{3 }and \frac{ -4 }{ 9 } are added$

21. LaynaMae

2/9 ?

22. surjithayer

$yes x ^{\frac{ 2 }{ 9 }}$

23. djaydeej88

use this property when you see a problem like #3 $x ^{m}/x ^{n} = x ^{m-n}$

24. LaynaMae

Okay

25. LaynaMae

So is 2/9 the answer then ? :o

26. djaydeej88

yep

27. LaynaMae

Okay thank you so much

28. surjithayer

note that answer is not 2/9 it is as i have given above x ^2/9

29. LaynaMae

Ohh okay well that makes more sense now . Thank YOU

30. surjithayer

yw