Expert: Paul Klarreich - 9/4/2011

Question
QUESTION: Dear Prof Paul

Some examples of Power / Exponent / Index

1.

2 raised to 3

2 ×2 ×2 =  8

2.

1.1 raised to 1.1

1.1 × 1.1 = 1.21

3.

0.5 raised to 3

0.5 × 0.5 × 0.5 = 0.125

4.

10 raised to 6

10 × 10 × 10 × 10 × 10 × 10 = 1000000

Is this right ?

i know 2.3 raised to 2.3 = 5.29

2.3 raised to 3.2 = ?

9.12 raised to 6.56 = ?

Are above legal operations ?

Thanks & Regards,
Prashant S Akerkar

ANSWER: Questioner:Prashant S Akerkar
Country:Maharashtra, India
Category:Advanced Math
Private:No
Subject:

Decimal Points Number Raised Power to Decimal Points

Number

Question:

Dear Prof Paul

Some examples of Power / Exponent / Index

1.

2 raised to 3

2 ×2 ×2 =  8

2.

1.1 raised to 1.1

1.1 × 1.1 = 1.21

>>>>>>>>>>> WRONG

3.

0.5 raised to 3

0.5 × 0.5 × 0.5 = 0.125

CORRECT

4.

10 raised to 6

10 × 10 × 10 × 10 × 10 × 10 = 1000000

Is this right ?

YES

i know 2.3 raised to 2.3 = 5.29

>>>>>>>>>> WRONG

2.3 raised to 3.2 = ?

9.12 raised to 6.56 = ?

Are above legal operations ?

YES, THEY ARE, AS LONG AS THE BASE IS POSITIVE.  USE

YOUR CALCULATOR.

Thanks & Regards,
Prashant S Akerkar


---------- FOLLOW-UP ----------

QUESTION: Dear Prof Paul

Thank you.

As you mention if they are valid operations,

But then how to compute without using a calculator but mathematically ?

is it possible using logarithms i.e using log tables or any other method ?

2.3 raised to 3.2 = ?

9.12 raised to 6.56 = ?

we have to consider four cases

Any Number raised to any Number.

1. Both Base and Exponent(Power) are Whole Numbers.

2. Both Base and Exponent(Power) are Decimal Point Numbers.

3. Base is Whole Number and Exponent(Power) is Decimal Point Number.

4. Base is Decimal Number and Exponent(Power) is Whole Number.

Thanks & Regards,
Prashant S Akerkar

Answer
As you mention if they are valid operations,

But then how to compute without using a calculator but mathematically ?

is it possible using logarithms i.e using log tables or any other method ?

YES.  Use your log tables:

X = 2.3 raised to 3.2

log X = 3.2 log 2.3.

Now look up log 2.3, multiply by 3.2, then find the antilog of the result.  You were supposed to study this in your intermediate algebra class, but I suppose they don't teach that any more.
...........................................
9.12 raised to 6.56 = ?

>> SAME THING.

we have to consider four cases

Any Number raised to any Number.

1. Both Base and Exponent(Power) are Whole Numbers.

2. Both Base and Exponent(Power) are Decimal Point Numbers.

3. Base is Whole Number and Exponent(Power) is Decimal Point Number.

4. Base is Decimal Number and Exponent(Power) is Whole Number.

ALL THESE CAN WORK THE SAME WAY.