Question

NEED MAJOR HELP! Please explain your answer with steps so I can understand how to do it too, thank you so much in advance.

Answer 1

The given expression ​
`((n^(3)) ^(2)(n^(6) )^(4) )/((n^(2)) ^(5) )` simplifies to
`{n^(20) }` using the rules of exponents, specifically the power of a power rule and the quotient rule.

To simplify the given expression
`((n^(3)) ^(2)(n^(6) )^(4) )/((n^(2)) ^(5) )` we can use the properties of exponents. The numerator contains two terms raised to powers, so we can apply the power of a power rule, which states that
`(a^(m) )^(n)` is equal to
`a^(mn)`.

Let's simplify each term step by step:

`(n^(3) )^(2)` can be simplified to
`n^(6)` because 2×3=6.

`(n^(6) )^(4)` can be simplified to
`n^(24)` because 4×6=24.

The denominator
`(n^(2) )^(5)` can be simplified to
`n^(10)` because 5×2=10.

Now, substitute these simplified terms back into the original expression:

`((n^(6)) (n^(24) ) )/((n^(10)) )`

To simplify further, we can use the quotient rule for exponents, which states that
`a^(m) / a^(n)`
`= a^(m-n)` and
`a^(m) * a^(n) = a^(m+n)`. Applying this rule, we get:

`(n^(30) )/(n^(10) )`
`= n^(30-10) = n^(20)`

So, the simplified expression is
`{n^(20) }\\`.