Question

8^1/2 : (8^1/6 * 9^3/2)

Answer 1

Прощу прошение за почерк)))))))

Answer 2

To simplify the expression 8^(1/2) : (8^(1/6) * 9^(3/2)), we need to apply the rules of exponents.

Let's break it down step by step:

First, we can simplify the expression within the parentheses: 8^(1/6) * 9^(3/2).

Using the rule (a^m)^n = a^(m*n), we can rewrite it as (8^(1/6) * (9^(1/2))^3).

Simplifying further, we have (8^(1/6) * 9^(1/2))^3.

Now, we can simplify the expression within the parentheses: 8^(1/6) * 9^(1/2).

To multiply these two terms with different bases, we can rewrite it as a single term with a common base.

Since 8 = 2^3 and 9 = 3^2, we can rewrite the expression as (2^3)^(1/6) * (3^2)^(1/2).

Applying the rule (a^m)^n = a^(mn), we have 2^(3(1/6)) * 3^(2*(1/2)).

Simplifying further, we get 2^(1/2) * 3^(1).

Now we can rewrite the original expression as 8^(1/2) : (2^(1/2) * 3).

To divide terms with the same base, we subtract the exponents: 8^(1/2) / 2^(1/2) * 3.

Using the rule (a^m)/(a^n) = a^(m-n), we have 8^(1/2 - 1/2) * 3.

Simplifying, we get 8^0 * 3.

Any number raised to the power of 0 is equal to 1, so 8^0 = 1.

The expression simplifies to 1 * 3 = 3.

Therefore, 8^(1/2) : (8^(1/6) * 9^(3/2)) is equal to 3.