Question

What is (99/100)^101 times (100/99)^100?

Answer 1

Answer:

99/100

Step-by-step explanation:

First of all recall that

$a^n\cdot b^n =(ab)^n$

Now we we will try to apply that formula for $a=99/100$ and $b=100/99$.

First rewrite $(99/100)^{101}=(99/100)\times (99/100)^{100}$

Now

$(99/100)\times (99/100)^{100}\times (100/99)^{100}\\=(99/100)\times ((99/100)\times (100/99))^{100}\\=(99/100)\times 1^{100}\\=(99/100)\times 1\\=99/100$