Question

Evaluate.

Answer 1

\[0.01^{-3/2}\]

Answer 2

\[{1 \over 0.01^{3 \over 2}} \]

Answer 3

Hint: Now you can put that in radical form and simplify!

Answer 4

(Put the denominator in radical form).
Remember:\[\large a^{b \over c} \implies \sqrt[c]{a^b}\]

Answer 5

And you'd also be able to simplify the denominator. Try it!

Answer 6

\[\sqrt[3]{0.01^2}\]

Answer 7

Or you could also think of this one:\[\large a^{3 \over 2} \implies a^{1 \over 2} \times a^{1 \over 2} \times a^{1 \over 2} = \sqrt{a} \times \sqrt{a} \times \sqrt{a} \]

Answer 8

\[0.01^{−3/2}=(0.1^{2})^{−3/2}=0.1^{(2\times-3/2)}\]

Answer 9

\[\large 0.01^{3 \over 2} \cdots \cdots \sqrt{0.01} \times \sqrt{0.01} \times \sqrt{0.01}\implies 0.1\times0.1\times0.1 \]

Answer 10

Those are enough of my hints :P

Answer 11

0.001??

Answer 12

Yeah!\[\Huge\ddot \smile \]

Answer 13

@ParthKohli my text gives the answer 1000.

Answer 14

No, not complete yet. Remember how we started with\[\large{1 \over 0.1^{3 \over 2}} \]?

Answer 15

According to our calculation, \(\large 0.1^{3 \over 2} = 0.001\). We now have to find:\[\large {1 \over 0.001} \]

Answer 16

And that, sir, gives us 1000 :)

Answer 17

mm I am lost.

Answer 18

Okay. Do you agree with this one?\[0.01\large^{-3 \over 2} \implies {1 \over 0.01^{3 \over 2}}\]?

Answer 19

yes

Answer 20

Now, do you agree with this?\[\large {1 \over 0.01^{3 \over 2} }\implies {1 \over 0.01^{1 \over 2} \times {0.01^{1 \over 2} \times 0.01^{1 \over 2}}} \]

Answer 21

that makes sense yes.

Answer 22

Now this one?\[1 \over \sqrt{0.01} \times \sqrt{0.01} \times \sqrt{0.01} \]

Answer 23

yes.

Answer 24

Now what is \(\sqrt{0.01}\)?

Answer 25

.1

Answer 26

Yes. That's right. That makes our work simplified to\[1\over 0.1 \times 0.1 \times 0.1 \]Now what is \(0.1\times0.1\times0.1\)?

Answer 27

.001

Answer 28

That's correct again! Now find what\[1 \over 0.001\]is.

Answer 29

I get it.

Answer 30

Great job!

Answer 31

thank you for your time.

Answer 32

You're welcome :)

Answer 33

if you re-write 0.01 as 1/100
the problem is
\[ (\frac{1}{100})^{-\frac{3}{2}} \]
flip the fraction to get rid of the minus sign on the exponent
you get
\[ 100^{\frac{3}{2}} \]
or
\[ (100^{\frac{1}{2}})^3 \]
now take the square root of 100 to get 10.
10^3 = 1000
(which is preferred to \(\frac{1}{0.001} \) )

Answer 34

@phi I just spent the last 5 mins doing the same thing lol.

Answer 35

as long as you get to the answer.