Rational Exponents

2012-12-20 11:10 pm

Evaluate, if possible.

please show all clear steps.

1) -81^1/2

2) 9^3/2 divide by 8^1/3

3) (fourth root of 6)( fourth root of 6^3)

4) 16^2/5 times 4^1/5

5) ((third root of 2)^15)^1/5

Thank you

回答 (1)

Pak Wai

2012-12-21 2:48 am

✔ 最佳答案

...For these questions, it might be no steps necessary like 1 + 1 = 2 ...
(At lease the first 2 questions are ones of such...)

1)
Not sure if you were asking -(81)^(1/2) or (-81)^(1/2)
-(81)^(1/2)
= -(3^4)^(1/2)
= -3^[4(1/2)]
= -3^2
= -9

(-81)^(1/2)
= [(3^4)(-1)]^(1/2)
= 3^[4(1/2)]i
= (3^2)i
= 9i

2)
9^(3/2)/8^(1/3)
= (3^2)^(3/2)/(2^3)^(1/3)
= 3^[2(3/2)]/2
= 3^3/2
= 27/2

3)
6^(1/4)(6^3)^(1/4)
= [6(6^3)]^(1/4)
= (6^4)^(1/4)
= 6

4) 16^(2/5)4^(1/5)
= (4^2)^(2/5)4^(1/5)
= 4^[2(2/5) + 1/5]
= 4^1
= 4

5)
{[2^(1/3)]^(15)}^(1/5)
= 2^[(1/3)(15)(1/5)]
= 2^1
= 2

參考: Myself

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