How do i convert radicals to exponents and negative exponents?

Question

I need to convert

a variety of fractions with exponents, exponents that are fractions, fractions that are a part of fractions, and radicals that are fractions

into radical form and negative exponents.


for example
I already converted 1/2^4 to 2^-4 in negative exponent form.

i hope this makes sense


PLEASE HELP ME ASAP IF YOU CAN

THANK YOU!

I already know those three main rules of exponents, i just am not sure on how to convert a fraction such as sqrt(81)/sqrt(9) into exponent and negative exponent form.

Answer 1

OK - here are the rules you'll need to use:
1) b^m * b^n = b^(m+n)
Multiplying numbers (with the same base) is done by adding exponents.
Example: b^3 * b^8 = b^(3+8) = b^11
2) 1) b^m / b^n = b^(m-n)
Dividing numbers (with the same base) is done by subtracting exponents.
Example: b^3 / b^8 = b^(3-8) = b^-5
3) (b^m)^n = b^(mn)
Raising to powers is done by multiplying exponents.
Example: (b^3^8 = b^(3*8) = b^24

You can use these to derive other useful equalities:
4) b^(-3) = b^(0-3) = b^0 / b^3 = 1 / (b^3)
A negative exponent in the top of a fraction turns into a positive exponent in the bottom and vice versa.
5) (a*b)^m = a^m * b^m
6) (a/b)^m = a^m / b^m

Radicals:
7) sqrt(x) = x^(1/2)
8) the cube root of x is x^(1/3)
9) the nth root of x is x^(1/n)

These equalities (and a bit of practice) will allow you to answer practically any exponent or radical question!

Answer 2

Hello
Let's say we have 2^(1/2) this means the square root of 2. Now 27^(2/3) means the square of the cube root of 27 or 3^2 or 9.

Using negative exponents we have

2/125^-(2/3) would be 2*125^(2/3) or 2*5^2 = 50.

Hope This Helps!!

Answer 3

a million) sqrt3 = ?3 = (3)^(a million/2) >========================< answer 2) sqrtx^3 = ?(x^3) = x^(3/2) >========================< answer 3) ^3sqrt(2x)^2 = [?((2x)^2)]^(a million/3) >========================< answer 4) (^3sqrt xy)^4 = [{?(xy)}^(a million/3)]^4 >========================< answer in addition Sokve the different.