3) Explain how the laws of exponents work with rational exponents and give at least one example of an expression containing rational exponents...
Please help.. I can't find the answer to this anywhere..
Since this is not my area of expertise, I searched Google under the key words "law of exponents" to get this:
http://www.google.com/search?client=safari&rls=en&q=law+of+exponents&ie=UTF-8&oe=UTF-8
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
why are exponents so complicated!!!! someone plz explain how to determine if an exponent is negative or positive D: D: D:
Certainly! The laws of exponents are a set of rules that help simplify and manipulate expressions involving exponents. These laws are applicable to both integer exponents (whole numbers) and rational exponents (fractions). Rational exponents can seem a bit complex, but they follow the same basic principles as integer exponents, just with a fractional twist.
Here are the key laws of exponents with rational exponents:
1. Product Rule: For any real numbers a and b, and any rational number m/n (where m and n are integers with n ≠ 0), a^(m/n) * b^(m/n) = (ab)^(m/n).
Example: Simplify (x^(2/3) * y^(1/3))^3
To simplify this expression, we first apply the product rule:
(x^(2/3) * y^(1/3))^3 = (xy)^(2/3) * y^(1/3) = (xy)^(2/3) * y^(1/3)
Keep in mind that the product rule allows us to combine the x and y terms together as (xy)^(2/3).
2. Quotient Rule: For any real numbers a and b, and any rational number m/n (where m and n are integers with n ≠ 0), a^(m/n) / b^(m/n) = (a/b)^(m/n).
Example: Simplify (x^(5/2) / y^(1/2))^2
Applying the quotient rule, we get:
(x^(5/2) / y^(1/2))^2 = (x^5 / y)^2 = x^(5*2) / y^2 = x^10 / y^2
3. Power of a Power Rule: For any real number a, and any rational numbers m/n and p/q (where m, n, p, and q are integers with n, q ≠ 0), (a^(m/n))^p/q = a^((m*p)/(n*q)).
Example: Simplify ((x^(2/3))^3)^2
Using the power of a power rule, we have:
((x^(2/3))^3)^2 = (x^(2/3 * 3))^2 = (x^2)^2 = x^(2*2) = x^4
These are just a few of the laws of exponents that apply to rational exponents. By learning and applying these rules, you can simplify and solve expressions involving rational exponents.