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Negative Exponents - Math is Fun
https://www.mathsisfun.com/algebra/negative-exponents.html
WEBA negative exponent means how many times to divide by the number. Example: 8-1 = 1 ÷ 8 = 1/8 = 0.125. Or many divides: Example: 5-3 = 1 ÷ 5 ÷ 5 ÷ 5 = 0.008. But that can be done an easier way: 5-3 could also be calculated like: 1 ÷ (5 × 5 × 5) = 1/53 = 1/125 = 0.008.
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Negative Exponents (Definition, Rules & Examples) |How to …
https://byjus.com/maths/negative-exponents/
WEBIn other words, the negative exponent describes how many times we have to multiply the reciprocal of the base. An example of negative exponents is 3 -2. Thus, 3 -2 is written as (1/3 2) Hence, the value of 3 -2 is 1/9. More examples of Negative exponents: 5 -1 is equal to ⅕. X -4 is written as 1/x 4.
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Negative exponents (video) | Khan Academy
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-pos-neg-exponents/v/negative-exponents
WEBIan Pulizzotto. 5 years ago. The negative sign on an exponent means the reciprocal. Think of it this way: just as a positive exponent means repeated multiplication by the base, a negative exponent means repeated division by the base. So 2^ (-4) = 1/ (2^4) = 1/ (2*2*2*2) = 1/16. The answer is 1/16.
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Negative Exponents - Rules, Fractions, Solve, Calculate - Cuemath
https://www.cuemath.com/algebra/negative-exponents/
WEBSolution: Use the negative exponent rule a -n = 1/a n. 2 -2 + 3 -2 = 1/2 2 + 1/3 2 = 1/4 + 1/9. Take the Least Common Multiple (LCM): (9 + 4)/36 = 13/36. Therefore, 2 -2 + 3 -2 = 13/36. Example 2: Solve: 1/4 -2 + 1/2 -3. Solution: Use the second rule with a negative exponent in the denominator: 1/a -n =a n. 1/4 -2 + 1/2 -3 = 4 2 + 2 3 =16 + 8 = 24.
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Negative exponents review (article) | Khan Academy
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-pos-neg-exponents/a/negative-exponents-review
WEBDefinition for negative exponents. We define a negative power as the multiplicative inverse of the base raised to the positive opposite of the power: x − n = 1 x n. Want to learn more about this definition? Check out this video. Examples. 3 − 5 = 1 3 5. 1 2 8 = 2 − 8. y − 2 = 1 y 2. ( 8 6) − 3 = ( 6 8) 3. Practice. Problem 1.
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Negative exponents - Math.net
https://www.math.net/negative-exponents
WEBNegative exponents. A negative exponent is equal to the reciprocal of the base of the negative exponent raised to the positive power. This is expressed as. where b is the base, and n is the power. In other words, a negative exponent indicates the inverse operation from a positive integer exponent: it indicates how many times to divide by the ...
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7.1: Negative Exponents - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(Arnold)/07%3A_Rational_Expressions/7.01%3A_Negative_Exponents
WEBFeb 21, 2022 · Simplify so that the resulting equivalent expression contains no negative exponents. Solution. Raising y to the \(−3\) means we have to cube and invert, so \(y^{−3} = 1/y^3\). \[\dfrac{x^2}{y^{-3}} = \dfrac{x^2}{\tfrac{1}{y^3}} \nonumber \] To divide \(x^2\) by \(1/y^3\), we invert and multiply.
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5.6: Negative Exponents - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Algebra/Beginning_Algebra/05%3A_Polynomials_and_Their_Operations/5.06%3A_Negative_Exponents
WEBOct 6, 2021 · Simplify: − 2x − 5y3 z − 2. Solution: Take care with the coefficient − 2; recognize that this is the base and that the exponent is actually + 1: − 2 = ( − 2)1. Hence the rules of negative exponents do not apply to this coefficient; leave it in the numerator. − 2x − 5y3 z − 2 = − 2x − 5y3 z − 2 = − 2y3z2 x5. Answer:
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3.7: Negative Exponents - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(Ellis_and_Burzynski)/03%3A_Basic_Operations_with_Real_Numbers/3.07%3A_Negative_Exponents
WEBNegative Exponent Definition. Example \ (\PageIndex {7}\) Example \ (\PageIndex {8}\) Example \ (\PageIndex {9}\) Example \ (\PageIndex {10}\) Example \ (\PageIndex {11}\) Example \ (\PageIndex {12}\) Practice Problem \ (\PageIndex {1}\) Practice Problem \ (\PageIndex {2}\) Practice Problem \ (\PageIndex {3}\) Practice Problem \ (\PageIndex {4}\)
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Negative exponent intuition (video) | Khan Academy
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-pos-neg-exponents/v/negative-exponent-intuition
WEBHow do negative exponents work? Let's build our intuition about why a^(-b) = 1/(a^b) and how this definition keeps exponent rules consistent. Continue the pattern of decreasing exponents by dividing by 'a', and see how it extends to zero and negative powers. While we're at it, we'll see why a^0 =1. Created by Sal Khan.
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