Please help answer..
What is the principle of powers? When solving a radical equation how do we use the principle of powers to eliminate radicals
Since this is not my area of expertise, I searched Google under the key words "principle of powers" to get this:
http://www.google.com/search?client=safari&rls=en&q=principle+of+powers&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/.
The principle of powers, also known as the exponentiation principle or power rule, states that if two powers are equal, their bases must also be equal. In other words, if a^m = b^m, where a and b are real numbers and m is a positive integer, then a = b.
When solving a radical equation, we can use the principle of powers to eliminate radicals. Here's how:
1. Identify the radical equation: Look for an equation that involves radicals, such as square roots (√) or higher roots (n√), where n is a positive integer.
2. Isolate the radical: Move the radical term to one side of the equation, isolating it.
3. Raising to a power: Raise both sides of the equation to a power that is the reciprocal of the index of the radical. For example, if you have a square root (√), raise both sides to the power of 2; if you have a cube root (∛), raise both sides to the power of 3, and so on.
4. Apply the principle of powers: Simplify the equation using the principle of powers. The goal is to eliminate the radical term.
5. Solve the resulting equation: Once the radical is eliminated, solve the resulting equation to find the value(s) of the variable.
6. Check for extraneous solutions: Since raising both sides of the equation to a power can introduce extraneous solutions (solutions that do not satisfy the original equation), it's essential to check your solutions in the original equation and discard any that do not work.
By following these steps and applying the principle of powers, you can successfully eliminate radicals and solve radical equations.