How would i evalute this?
simplyfying expressions with rational exponents. 6 square root (3^3)^4*(3^2)^4. the answer is 81. any ideas on how to do that?
You must mean
[(3^3)^4*(3^2)^4]^(1/6)
which meants the sixth root of what is in brackets. You can rewrite it as
[3^12*3^8]^(1/6)
= 3^(20/6)= 3^(10/3) = 38.9
I don't agree with your book's answer.
Tf it was the 1/6 root of [(3^3)^4*(3^3)^4] THAT would be 3^4 = 81. .
Agree exactly with drwls, just spent about ten minutes reverse engineering it to try to figure out what the problem statement was.
To evaluate the expression 6√(3^3)^4 * (3^2)^4, you can follow these steps:
1. Start by simplifying the exponents within each set of parentheses separately. Recall that when you raise an exponent to another exponent, you multiply the exponents.
- In the first set of parentheses, (3^3)^4, simplify the exponent: 3^3 = 27, and 27^4 = 531,441.
- In the second set of parentheses, (3^2)^4, simplify the exponent: 3^2 = 9, and 9^4 = 6,561.
2. Substitute the simplified exponents back into the original expression to get: 6√(531,441) * (6,561).
3. Evaluate the square root of 531,441. The square root of 531,441 is 729. (Since 729 * 729 = 531,441).
4. Multiply 6 * 729 to get 4,374.
Therefore, the final answer is 4,374.