I am doing a worksheet for my alg. 2 class and in the worksheet it says:
'Simplify the expression. Assusme all variable are positive.' the problem is perentheses, square root of six times the power of 3 square root of six perentheses power of six!
To simplify the expression, let's break it down step by step:
1. Start with the expression inside the parentheses:
(sqrt(6) * (3 * sqrt(6))) ^ 6
2. Simplify the expression within the parentheses:
Inside the parentheses, we have 3 multiplied by the square root of 6, which can be written as 3 * sqrt(6).
3. Next, simplify the expression within the square root:
The square root of 6 multiplied by the square root of 6 gives us the square root of (6 * 6), which simplifies to the square root of 36.
4. Continue with the simplification:
After simplifying the inner expression, we are left with (sqrt(6) * 3 * sqrt(6))^6, which simplifies to (3 * sqrt(6))^6.
5. Simplify the expression inside the parentheses using the power rule:
To raise a product to a power, we can raise each factor to that power. In this case, we have (3^6 * (sqrt(6))^6).
6. Evaluate the powers:
3 raised to the power of 6 is 3 * 3 * 3 * 3 * 3 * 3, which is 729.
(sqrt(6))^6 is equal to (6^(1/2))^6, which simplifies to 6^(6/2), and then becomes 6^3.
So, (sqrt(6))^6 is equal to 6^3, which is 6 * 6 * 6, or 216.
7. Multiply the simplified factors:
Now that we have simplified each factor, we can multiply them together: 729 * 216.
8. Calculate the final result:
Multiply 729 by 216 to get the simplified result. The answer should be 157,464.
So, the simplified expression is 157,464.