Fractional Exponents - Discovery Education

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SD School Pre-Algebra Program 3: Roots and Rational Numbers QuikNotes A cube root like a square root, except the number is multiplied 3 times to get another whole number. The cube root of 729 equals 9, because 9 x 9 x 9 = 729. Student Notes The 3 in the arm of the radical signals to us that we’re looking for the cube root. 3 729 = 9 Whenever we have a cube root, or some other odd root, it’s possible for us to end up with a negative number under the radical. This is because whenever we multiply an odd number of negative integers together, our answer will be negative. 3 −8 =−2 because (−2) × (−2) × (−2) =−8 If there is a negative number under the radical and we’re looking for an even root, like the square root of negative 4, it is undefined. The reason we say it’s undefined is because we can’t find one real number multiplied by itself to equal negative 16. This is different than when we have a negative sign in front of our radical. Remember that this means we’re looking for the negative of the square root of a number, which we can do for any number. So, here the negative square root of 16 is -4. − 16 =−4 −16 is undefined Raising a number to the fourth power means multiplying that number four times. So, the fourth root of a number means finding the number that when multiplied 4 times gives us our original number. For example: 4 16 = 2 because 2 × 2 ×2 × 2 = 16 When we’ve got a number with an exponent that’s a simple fraction, like 3 to the one-half power, it just means the square root of 3. We look at what number is in the denominator and take that root of our base number. 1 3 2 = 3
SD School Pre-Algebra Program 3: Roots and Rational Numbers QuikNotes If the same kind of exponent is negative, take the reciprocal of the base number, and then make the exponent positive. a 1 − n = a 1 1 n = n 1 a Student Notes 1 − 1 1 1 3 8 = = = 1 3 8 2 3 8 When given a fractional exponent where the numerator is not a 1: 1. Raise the base number to the power of the numerator. 2. Take the root as signaled by the denominator. 3 5 4 = 4 3 5 4 3 5 5 = 64 = 2 2 Irrational numbers are decimals that go on forever and don’t repeat. An example would be the number pi (ð). A repeating decimal is a rational number. An example is the fraction, 1/3. It is equal to 0.3333333… The repetition of 3 goes on forever. A terminating decimal is also a rational number. Rational, irrational, and repeating decimals are all real numbers. An inequality is a mathematical expression that is unbalanced. Statements like 5 is greater than 3, or 4 is less then 7 are considered inequalities because the two sides don’t balance. 5 > 3 4 < 7
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Fractional Exponents - Discovery Education

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