Question

What is the value?

Answer 1

What is the value of \[(2)^{2.4}\]

Answer 2

@dan815 @ganeshie8

Answer 3

5.2780316430916

Answer 4

Could you tell me the process?

Answer 5

Basic Exponent Laws
am+n = am * an
am-n = am / an
am*n = (am)n
(a * b)n = an * bn
(a / b)n = an / bn
a-n = 1 / an
a1 = a
a0 = 1
00 = 1 (definition)
Examples:

base 2 with the exponent 5: 25 = 32
base -2 with the exponent 5: (-2)5 = -32
base 2 with the exponent 6: 26 = 64
base -2 with the exponent 6: (-2)6 = 64
base 2 with the exponent 1/2: 21/2 = 1.414
base -2 with the exponent 1/2: (-2)1/2 = 1.414i (i means imaginary)

Answer 6

I know the basic laws of exponents but I can't understand the matter after that. I think you can find the value with logarithms

Answer 7

go to http://www.purplemath.com/modules/logs.htm
mabey this will help

Answer 8

Hey Dan, do you know this one?

Answer 9

@mathmale

Answer 10

If you want to evaluate \[(2)^{2.4}\] manually (that is, without a calculator), you could re-write that exponent, 2.4, as 12/5 (check that out, please). Then, according to rules of exponents, \[(2)^{2.4}=(2)^{\frac{ 24 }{ 10 }}=2^{\frac{ 12 }{ 5 }}. \]

Answer 11

Yeah I know till that step. What to do after that?

Answer 12

I don't see a way to simplify this further.

This expression could be evaluated by (1) finding the 12th power of 2, and then finding the 5th root of your result.

If you're allowed to use a calculator for evaluating this type of problem, type in 2^2.4 ENTER.

Answer 13

Note that 2^12 = (2^4)^3=(16)^3.

But this last result isn't a perfect fifth power.

Answer 14

Okay. Thankyou

Answer 15

Glad to be of help.

Answer 16

2^12/5 = (2^1/5)^12
for...
x=2^1/5
x^5-2=0
Euler's Method
let G be initial Guess
y=x^5-2
y'=5x^4