What is the value of 10^0.20?How do u solve a base which has an indice in fractions i.e. 10^0.20?

Question

How do go about solving 10^0.20 or say 5^0.30

Answer 1

10^0.2 is the fifth root of ten.

Let X = 10^0.2

Then -- what is X^5?

X^5 = (10^0.2)^5 = 10 ^(0.2*5) = 10^1 = 10

So -- 10^0.2 is the number such that when you raise it to the fifth power is equal to ten.

Answer 2

The rule for indices which are fractions is that x^(a/b) = ^b√(x^a) . The b is meant to be superscripted but the computer won't let me do that...so in words, x^(a/b) = the bth root of x^a.

For example:
16^(1/2) = ²√(16¹)
= √16
= 4 or -4

27^(3/2) = ²√(27³)
=√19683.

So 10^0.2
= 10 ^ (1/5)
Which is the 5th root of 10. Gotta use a calculator, as far as I know.

Similarly, 5^0.3
= 5^(3/10)
= the 10th root of 5³, or 125.
But I find it much easier just to put 5^0.3 in the calculator!

Answer 3

10^0.20 can be written as 10^(1/5)

where: 1 (numerator) is the exponent of the base and 5(denominator) is the index of the radical sign

thus, 10^0.20 can also be expressed as

> the 5th root of 10 raised to 1

with this, you can now get the value of the term using the calculator or the manual way of getting its value, which is of course not practical to use.

Answer 4

ok so .2 is the same as 1/5
so 10^ .20 = 10^1/5 which fifth root of 10
and 5^.30 = 10^ 3/10 which means u have to cube the 10 and then take the 10th root of it.

Answer 5

10^.2 is the same as 10^(1/5) which is another way to say the fifth root of 10. You could just plug it into your calculator to get the answer or you could try to figure out what number is multiplied by itself 5 times to equal 10, which wont come out to a pretty number