Question

Higher roots with exponents?

Answer 1

How do I simplify?

Answer 2

factor x^{16}
remember exponent rules \[\huge\rm x^m \times x^n = x^{m+n}\]

Answer 3

so you can write x^5 times x^5 times x^5 times x which is equal to ??

Answer 4

\[\huge\rm x^5 \times x^5 \times x^5 \times x= x^?\]

Answer 5

when we multiply same bases we should add their exponents :-)
exponent rules \[\huge\rm x^m \times x^n = x^{m+n}\]

Answer 6

So, would it look like this?

Answer 7

\[\huge\rm x^5 \times x^5 \times x^5 \times x= x^?\]
you didn't answer my question :(

Answer 8

Wouldn't it be x^16? (I have such a problem with these >.< )

Answer 9

yes right

Answer 10

now factor them under the 5th root \[\huge\rm \sqrt[5]{x^5 \times x^5 \times x^5 \times x }\]
just like square can cancelz out with square same idea here
&that's why we have to make a pair of five exponent so we cancel them with 5th root solve that

Answer 11

you can convert root to exponent \[\huge\rm \sqrt[n]{x^m}= x^\frac{ m }{ n }\]

Answer 12

Oh! Alright! I didn't know that! (Please excuse my ineptitude... I'm a history person, lol....)

Answer 13

Huh! Would it be X^4, then?

Answer 14

convert 5th root to exponent

Answer 15

When you convert to an exponent, Each 5th root would result in one, correct? Making it just X instead of x rasied to a power.

Answer 16

yes right but x is same as x to the one power x^1

Answer 17

True. So because each x factor would result in x^1, I'm thinking the end result would be X^4.

Answer 18

\[\huge\rm \sqrt[5]{x^5 \times x^5 \times x^5 \times x }\]
\[\huge\rm x^\frac{5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 1 }{ 5 }\]
so it should be like this

Answer 19

\[\huge\rm \sqrt[5]{x^5 \times x^5 \times x^5 \times\color{reD}{ x} }\]
red x doesn't have power so you cannot cancel 5th root. it should stay under the 5th rot
\[\huge\rm x^\frac{5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 1 }{ 5 }\]
so it should be like this

Answer 20

Omg! It makes sense now! Would it be x^3 5^(sqrt) x? (I'll model that answer in a second. Thanks for your patience ^^)

Answer 21

yes!

Answer 22

np :-)

Answer 23

To confirm, like this?

Answer 24

yes