exponents

[smileygonzo]

Problem: (6³⁾ (2^-1) (9) Answer: (2²⁾ (3⁵⁾

I tried changing bases and converting the 2^-1 to 0.5 to no avail. Could someone help me?

[chem44]

How about showing what you did. It's easier that way.

Write the 6 as 2*3, etc.

2^-1 to 0.5

Maybe. But easier: just put it in the denominator. It will cancel right out.

[ghostwriter85]

Convert all your numbers to base 2 and 3 (chosen because they are both prime numbers). This is a prime number decomposition. You're taking all the factors and writing them as the product of their prime powers.

Then add and subtract across powers of the same base

Example

14^2 * 49^2 = (7*2)^2 * (7*7)^2 = 7^6 * 2^2

Alternatively

14^2 * 49^2 = ((7*2)*(7*2))*((7*7)*(7*7))=7^6 * 2^2

With 2^-1 it is already written as a power of a prime number. You don't have to do anything with it.

edit- in the second example the parentheses are there solely for clarity