Question

Simplify. n 6 · n 5 ÷ n 4 · n 3 ÷ n 2 · n

Answer 1

Answer: $n^{9}$

Step-by-step explanation:

Given expression: $n^6\cdot n^5\div n^4\cdot n^3\div n^2\cdot n$

The law of exponents are given by :_

$a^m\cdot a^n=a^{m+n}\\\\a^m\div a^n=a^{m-n}$

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

$n^{6+1+1+1}\\\\=n^{9}$

Answer 2

Answer:

The given expression  $n^6\cdot n^5\div n^4\cdot n^3\div n^2\cdot n$ is $n^9$            

Step-by-step explanation:

Given : Expression  $n^6\cdot n^5\div n^4\cdot n^3\div n^2\cdot n$

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

Consider the given expression  $n^6\cdot n^5\div n^4\cdot n^3\div n^2\cdot n$

Rewrite it in simpler form, we have,

$n^6\cdot\frac{n^5}{n^4}\cdot \frac{n^3}{n^2}\cdot n$

Apply exponent rule, $\:a^b\cdot \:a^c=a^{b+c}$, we have,

$n^6n=\:n^{6+1}$

$=\frac{n^5}{n^4}\cdot \frac{n^3}{n^2}n^{7}$

Apply exponent rule, $\frac{x^a}{x^b}=x^{a-b}$

$\frac{n^5}{n^4}=n^{5-4}$

$\frac{n^3}{n^2}=n^{3-2}$

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 $n^6\cdot n^5\div n^4\cdot n^3\div n^2\cdot n$ is $n^9$