How to Simplify Exponents & Radicals
Exponents are algebraic expressions we use to simplify larger numbers such as 210 = 1024, and radicals are expressions we use to make larger numbers smaller, such as 10√1024 = 2. Being able to simplify exponential and radical expressions can be key in making a harder looking equation much simpler to solve.
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Instructions
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Multiply exponents. When multiplying exponents, adding the exponents together will give you a new exponent to work with. For example: x2 * x3 will yield x5, when you add the exponents 2 and 3 together.
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Divide exponents. When dividing exponents, you subtract the bottom exponent from the top. For example: x3/x2 will yield x, when you subtract the exponent 3-2. When expressions become more difficult like x2y3z5/xyz, you will need to incorporate the idea of canceling. You can only cancel like variables, like x from x and y from y. In the example above, the answer will be xy2z4, when you cancel 2-1 with x, 3-1 with y, and 5-1 with z.
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Understand factors. To simplify a radical, you have to have a basic understanding of how factoring works. Factoring splits a number into smaller factors that equal that number. For example, 100 can be split into the factors of 4 and 25, since when multiplied equals 100.
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Simplify radicals. Using the idea of factoring, simplify a radical by splitting it into a factor whose root can be taken. Using 100, you can split it into 4 and 25, two numbers that are square numbers. Therefore, √100 = √4 * √25 = 2 * 5 = 10, which is the square root of 100. Using another example, √80 has the factors of 16 (which is a square number) and 5 (which isn't a square number). √16 * √5 = 4√5.
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Tips & Warnings
If you are unaware of the idea of factoring numbers, research and understand factors before attempting to simplify a radical.
