How do you simplify $15^4/15^6$ ?

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Answer 1 · 2016-05-25T20:03:42

$1/225$

Consider the example of $a^2$ , this is $a^1xxa^1=a^2=a^(1+1)$

So $a^5$ , if so chosen, could be written as $a^(2+3)=a^2xxa^3$

$color(blue)("Back to your question")$

$color(brown)("Method 1")$

Write $15^4" as "15^4 xx1$

Write $15^6" as "15^(4+2) = 15^4xx15^2$

So $15^4/15^6=(15^4xx1)/(15^4xx15^2)$

This is the same as $15^4/15^4xx1/15^2$

But $15^4/15^4=1$ giving

$color(brown)(15^4/15^6=1/15^2 = 1/225)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$color(brown)("Method 2")$

Consider the example: $1/a^2 = a^(-2)$

Write $15^4/15^6" as "15^4xx15^(-6)$

$color(brown)(=15^(4-6)=15^(-2) = 1/15^2 =1/225)$

How do you simplify 15^4/15^615^4/15^6?