Can someone please help me with these problems?
Write (27a^-3)^-2/3 in simplest form.
Solve log(6x+11)=2.
thanks
Let me see your work, we can start from there.
Alright! :D
(27a^-3)^-2/3
=the cubed root of (27a^-3)^-2
=the cubed root of 27^-2a^6
i figured out how to do the second one, so nevermind that one
Great start on simplifying the first problem! You correctly applied the exponent rule for negative exponents and brought the base (27) and variable (a) to the numerator by changing the sign of the exponents.
Now, let's continue simplifying (27a^-3)^-2/3.
To simplify further, we need to simplify the expression inside the cubed root.
(27^-2a^6) can be rewritten as (1/27^2 * a^6).
Now, let's distribute the cubed root (or the exponent of 1/3) to each term within the parentheses:
(1/27^2 * a^6)^(1/3)
Using the exponent rule for multiplying exponents, we can rewrite this as:
(1^(1/3) / (27^2)^(1/3)) * (a^6)^(1/3)
Simplifying further:
(1/27^(2/3)) * a^(6/3)
When we simplify the exponents, we get:
(1/27^(2/3)) * a^2
Finally, we can write the answer in simplest form as:
a^2 / 27^(2/3)
Therefore, (27a^-3)^-2/3 simplifies to a^2 / 27^(2/3).
If you have any further questions or need additional assistance, feel free to ask!