Question

⁴√a : a( в степени 1\2)

Answer 1

Ответ:

[4]√(1/a)

Объяснение:

[4]√a:a^1/2=a^(1/4:a^1/2=a^(1/4-1/2)=a^((1-2)/4))=a^-1/4=[4]√1/a

⁴√a=[4]√a

Answer 2

To understand the expression ⁴√a : a( в степени 1\2), let's break it down step by step.

1. ⁴√a: This represents the fourth root of 'a.' The fourth root of a number 'a' is a value 'x' such that x^4 = a. In other words, it is the number that, when raised to the power of 4, gives 'a' as the result.

2. a( в степени 1\2): This is 'a' raised to the power of 1/2. In mathematics, raising a number to the power of 1/2 is equivalent to finding the square root of that number. So, 'a' raised to the power of 1/2 is √a, which represents the square root of 'a.'

Therefore, the expression ⁴√a : a( в степени 1\2) can be rewritten as (fourth root of 'a') divided by (square root of 'a'):

⁴√a : a( в степени 1\2) = ⁴√a / √a

To simplify this expression, remember that any positive number 'a' raised to the power of 1/n (where n is a positive integer) can be written as the nth root of 'a'. So, √a is the same as a^(1/2). With that in mind, we have:

⁴√a / √a = ⁴√a / a^(1/2)

Now, we can simplify this further by using the rule of exponents, which states that when you divide two numbers with the same base, you can subtract their exponents:

⁴√a / a^(1/2) = a^(1/4 - 1/2)

Now, find a common denominator for 1/4 and 1/2, which is 2:

a^(1/4 - 1/2) = a^(2/4 - 2/4) = a^(-1/4)

Finally, a^(-1/4) represents the fourth root of 'a' in the denominator, so it can be written as 1/(⁴√a):

a^(-1/4) = 1/(⁴√a)

So, the simplified expression is:

⁴√a : a( в степени 1\2) = 1/(⁴√a)