1. (12g^4)^-1 (work check)
12g^-4 = 1/(12g^4)
2. (2y^4)^-3 (need help)
#1 ok
#2 Hmmm. If you got 1, don't see why 2 is any problem
(2y^4)^-3 = 1/(2y^4)^3 = 1/(8y^12)
How did you get (8y^12)?
(2y^4)^3 = (2)^3 * (y^4)^3 = 8 y^12
Just as (2*5)^2 = 2^2 * 5^2 = 4*25 = 100
Thanks, I get it now. One more...
(r^2 s)^5
To simplify the expression (2y^4)^-3, we need to apply two properties of exponents. First, the negative exponent property states that any term with a negative exponent can be rewritten by taking the reciprocal of the term and making the exponent positive. Second, the power of a power property states that when we have an exponent raised to another exponent, we can multiply the exponents.
Let's break it down step by step:
Step 1: Apply the negative exponent property
(2y^4)^-3 = 1 / (2y^4)^3
Step 2: Apply the power of a power property
(2y^4)^3 = 2^3 * (y^4)^3 = 8 * y^(4*3) = 8 * y^12
Step 3: Take the reciprocal
1 / (2y^4)^3 = 1 / (8 * y^12)
Therefore, the simplified expression for (2y^4)^-3 is 1 / (8 * y^12).