Need help computing 10^999 × 5^-998 × 2^-997

[Argile1845]

Need help computing 10^999 × 5^-998 × 2^-997

Just tell me how to go about it and I can solve it myself. Not sure what to do if both the bases and the exponents are different.

 

[tkhunny]

2 * 5 = 10

 

[pka]

Just tell me how to go about it and I can solve it myself. Not sure what to do if both the bases and the exponents are different.

\(\large 10^{999}=2^{999}\cdot 5^{999}\cdot 2^{-997}\cdot 5^{-998}=?\)

 

[HallsofIvy]

Or \(\displaystyle 2^{-997}\times 5^{-998}= 2^{-997}\times 5^{-997}\times 5^{-1}= 10^{-997}\times \frac{1}{5}\).

(I feel compelled to point out that
\(\displaystyle 10^{999}= 2^{999}\times 5^{999}\)

NOT \(\displaystyle 2^{999}\times 5^{999}\times 2^{-997}\times 5^{-998}\)!)

 

[Argile1845]

So the entire question would look like this
2^999 × 5^999 × 5^-998 × 2^-997?

The twos would cross each other out and become 2^2 × 5?
That would be 20?

 

[Deleted member 4993]

So the entire question would look like this
2^999 × 5^999 × 5^-998 × 2^-997?

The twos would cross each other out and become 2^2 × 5?
That would be 20?

Correct ...