The meaning of powers which are negative or fractions.

  • From: Terry
  • Subject: Powers

How do I work out these:

  1. 243^(3/5)
  2. 8^(-2/3)

 

Maths Help suggests:

Fractional Powers

The numerator (top part) of the fraction behaves as a normal power,
and the denominator (bottom part) represents a root.

For example, the number 64^(3/4) means:

Take 81, cube it, then find the fourth root.
        or
Take 81, find the fourth root, then cube it.

I would recommend the second way, because the numbers will remain smaller
and therefore easier to work with:

81^(3/4) = (4th root of 81) cubed = 27

So you can work out the answer to your question in the same way:

243^(3/5) = (5th root of 243) cubed     Answer at the end...

Negative Powers

A negative power represent a reciprocal (1 divided by).

For example, the number 2-1 means:
the reciprocal of 2, or ½.

So you can work out the answer to your question in the same way:

8^(-2/3) = reciprocal of (cube root of 8) squared

So the answers to your questions are 27 and ¼ respectively.

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