Question

Find the quotient.


`(5^6)/(5^5)`

Answer 1

to the risk of sounding redundant.


`\bf a^(-n) \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^(-n) \qquad \qquad a^n\implies \cfrac{1}{a^(-n)} \\\\ -------------------------------\\\\ \cfrac{5^6}{5^5}\implies 5^6\cdot 5^(-5)\implies 5^(6-5)\implies 5^1\implies 5`

Answer 2

We can solve this problem by using the laws of exponents. The laws of exponents state:


`(x^(n) )/(x^(y) )` =
`x^(n-y)`

We can use this law in our situation. The answer here, using the laws of exponents, is
`5^(6-5)` or 5.