Question

Simplify.

n 6 · n 5 ÷ n 4 · n 3 ÷ n 2 · n

Answer 1

The given expression
`n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n` is
`n^9`

Explanation:

Given : Expression
`n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n`

We have to write the simplified form for the given expression
`n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n`

Consider the given expression
`n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n`

Rewrite it in simpler form, we have,

`n^6\cdot(n^5)/(n^4)\cdot (n^3)/(n^2)\cdot n`

Apply exponent rule,
`\:a^b\cdot \:a^c=a^(b+c)`, we have,

`n^6n=\:n^(6+1)`

`=(n^5)/(n^4)\cdot (n^3)/(n^2)n^(7)`

Apply exponent rule,
`(x^a)/(x^b)=x^(a-b)`

`(n^5)/(n^4)=n^(5-4)`

`(n^3)/(n^2)=n^(3-2)`

Expression becomes,

`=n^7nn`

Again apply exponent rule, we have,

`\:a^b\cdot \:a^c=a^(b+c)`

`=n^(1+1+7)=n^9`

Thus, The given expression
`n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n` is
`n^9`

Answer 2

Answer:
`n^(9)`

Explanation:

Given expression:
`n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n`

The law of exponents are given by :_

`a^m\cdot a^n=a^(m+n)\\\\a^m/ a^n=a^(m-n)`

Using PEDMAS, first we solve division, we get

`n^6\cdot n^(5-4)\cdot n^(3-2)\cdot n\\\\=n^6\cdot n\cdot n\cdot n`

Now, using product law of exponent we get

`n^(6+1+1+1)\\\\=n^(9)`