Fractional Powers

**CSG18** · March 6th 2010, 04:27 AM

Hi,

I did a non-calculator past paper and I got to this answer:

25 ×(〖1/5)〗^9

however when I had checked the mark scheme the answer that was given was simplified further (and worth an extra mark) to:

1.28*10^-5

How can I get to that answer by hand?

**Soroban** · March 6th 2010, 04:54 AM

Hello, CSG18

I did a non-calculator past paper and I got to this answer:

. . $25 \times \left(\frac{1}{5}\right)^9$

However, the answer given was simplified further (and worth an extra mark) to:

. . $1.28 \times 10^{-5}$

How can I get to that answer by hand?

By hand? . . . ack!

We have:. $5^2 \times \frac{1}{5^9} \;=\;\frac{1}{5^7}$

Then: . $\left(\frac{1}{5}\right)^7 \;=\;(0.2)^7 \;=\;\left(2\times 10^{-1}\right)^7 \;=\;2^7 \times \left(10^{-1}\right)^7 \;=\;128 \times 10^{-7} \;=\;1.28 \times 10^{-5}$

**CSG18** · March 6th 2010, 06:21 AM

Thanks Soroban!

That is a good way to reach that answer - very straight forward.

Thanks again.

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