SOLUTION: Simplify 20^10/40^5 20 to the 10th divided by 40 to the 5th

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Question 1207258: Simplify
20^10/40^5 20 to the 10th divided by 40 to the 5th
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
20^10 / 40^5 equals:

2^10 * 10^10) / (2^5 * 2^5 * 10^5) equals:

(2^10 * 10^10) / (2^10 * 10^5) equals:

2^10 / 2^10 * 10^10 / 10^5 equals:

10^5 which is equal to 100,000.

you can use your calculator to confirm.

calculator tells you (20^10) / 40^5 = 100,000.

the concepts used are:

(a * b)^x = a^x * b^x

(a^x * b^x) / (a^y * b^y) = (a^x / a^y) * (b^x / b^y)

you can see the first concept in 20^10 = (2 * 10) ^ 10 = 2^10 * 10^20.

you can see the second concept in (2^10 * 10^10) / (2^10 * 10^5) = 2^10 / 2^10 * 10^10 / 10^5.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


20%5E10%2F40%5E5

Break the denominator into two parts:
20%5E10%2F%28%2820%5E5%29%282%5E5%29%29

Simplify the powers of 20 in the numerator and denominator:
20%5E5%2F2%5E5=%2820%2F2%29%5E5=10%5E5

ANSWER: 10^5, or 100,000