[Hard] Indices question

Question

[Hard] Indices question

0

1052

6

+9675

Simplify the expressions. Round off to 3 significant figures if necessary. Give the answer in scientific notation.

2. (f)

$\sqrt[3]{1.25\times10^{200}}$

This is one of the questions of the Law of Indices quiz which I have taken today. No one in the class could do this :( . Thought I would get full marks again :(

(P.S. :I get full marks in nearly every quizes, but not tests)

(P.P.S. : I nearly got full marks in my last yearly exam. Ended up with a score 91 out of 94.)

MaxWong Sep 14, 2016

edited by MaxWong Sep 14, 2016

Best Answer

6⁺⁵ Answers

#1

+33658

+10

Best Answer

Hint:

5^3 = 125

(10^66)^3 = 10^198

.

Alan Sep 14, 2016

4 Online Users

Alan · Answer 1 · 2016-09-14T12:38:46

Hint:

5^3 = 125

(10^66)^3 = 10^198

.

Melody · Answer 2 · 2016-09-14T12:44:54

#2

+118703

+5

Come on Max, cant you work it out from Alan's answer - or do you need more help??

I thought Alan's answer was a good one :))

If you need more help just say so :))

Melody Sep 14, 2016

#3

+9675

+5

Is it 5 x 10^66?

MaxWong Sep 14, 2016

#4

+118703

+5

\sqrt[3]{1.25\times10^{200}}

$\sqrt[3]{1.25\times10^{200}}\\ =\sqrt[3]{1.25}\times\sqrt[3]{10^{200}}\\ =\frac{\sqrt[3]{125}}{\sqrt[3]{100}}\times\sqrt[3]{10^{198}}*\sqrt[3]{100}\qquad \text{I have used Alan's hit here}\\ =\frac{\sqrt[3]{125}}{1}\times\sqrt[3]{10^{198}}*1\\ =5\times 10^{66}\\$

So yes your answer is correct :)

Melody Sep 14, 2016

Guest · Answer 3 · 2016-09-14T01:30:46

Come on MaxWong, a very smart young man like you couldn't figure this one out!!? I just don't believe it:

[1.25 x 10^200]^1/3 =[125 x 10^198]^1/3 =5 x 10^66

[Hard] Indices question

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