Write each of the following numbers as a power with a rational exponent:
√2
5√(6^2)
so 1. is 2^1/2, idk about the second one
6^ 2/5 sorry I got it
good!
the 2nd:
5√(6^2)
= 5√36
= 5*6
= 30
To write a number as a power with a rational exponent, we need to express it using the rules of exponents. Let's start with each number:
1. √2:
To write √2 as a power with a rational exponent, we need to find a rational number that, when raised to that exponent, equals √2. In this case, we can express √2 as (2^(1/2)). So, √2 can be written as 2^(1/2).
2. 5√(6^2):
To express 5√(6^2) as a power with a rational exponent, we first simplify the expression under the radical, which is 6^2 = 36. Then, we can write it as 5^(1/√36).
However, we can simplify this further. Since (√36 = 6), we can rewrite it as 5^(1/6).
In summary:
√2 can be written as 2^(1/2)
5√(6^2) can be written as 5^(1/6)