write (27a^-3)^(-2/3) in simplest form.
solve log(6x+11)=2
please and thanks
I am not going to give you the answers. I will be happy to critique your work.
In the first, remember that (a^b)^c= a^bc
I am not looking for the answers.
And I told you:
I'm not quite sure what to do for the first, but this is what I tried to do:
(27a^-3)^(-2/3)
=the cubed root of (27a^-3)^-2
=the cubed root of 27^-2*a^6
and
what is the antilog?
but you didn't reply.
I apologize for not responding to your previous message. Let's walk through the steps to simplify the expression (27a^-3)^(-2/3).
To simplify the expression, you need to apply the properties of exponents. The property that applies here is the power of a power. According to this property, (a^b)^c is equal to a^(b * c).
Given the expression (27a^-3)^(-2/3), we can simplify it as follows:
Step 1: Apply the power of a power property.
(27a^-3)^(-2/3) = 27^(-2/3) * (a^-3) * (-2/3)
Step 2: Simplify 27^(-2/3).
To simplify 27^(-2/3), we can express 27 as 3^3, then apply the power property of negative exponents.
27^(-2/3) = (3^3)^(-2/3) = 3^(-2) = 1/3^2 = 1/9
Step 3: Simplify (a^-3) * (-2/3).
To simplify (a^-3) * (-2/3), we can multiply the exponents and apply the negative exponent property.
(a^-3) * (-2/3) = a^(-3 * (-2/3)) = a^2
So, the simplified form of (27a^-3)^(-2/3) is 1/9 * a^2.
Moving on to the logarithmic equation log(6x + 11) = 2, we want to solve for x.
To solve this equation, we can use the property of logarithmic functions that states: If log(a) = b, then 10^b = a.
In the given equation, log(6x + 11) = 2, we can rewrite it as:
10^2 = 6x + 11
Simplifying further:
100 = 6x + 11
Now, let's isolate x:
100 - 11 = 6x
89 = 6x
To solve for x, divide both sides of the equation by 6:
89/6 = x
You can leave the answer as 89/6 or convert it to a mixed number or a decimal depending on the desired form.
I hope this explanation helps you understand how to approach these types of problems. If you have any further questions, feel free to ask!