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  • How do you compute negative numbers to fractional powers?
    A negative base is a point of conflict between the three commonly used meanings of exponentiation For the continuous real exponentiation operator, you're not allowed to have a negative base For the discrete real exponentiation operator, we allow fractional exponents with odd denominators, and $$ (-a)^ {b c} = \sqrt [c] { (-a)^b}= \left ( \sqrt [c] {-a} \right)^b = (-1)^b a^ {b c} $$ (and
  • I need intuition about fraction exponents, like $4^{1. 2}$. What . . .
    What happens to the number with a fraction exponent when we try to represent it only using numbers and basic operations (like $+$, $-$, $\div$, and $\cdot$)? $4^ {1 2} = 4*4^ {0 2}$; but there's still a fractional exponent, $0 2$, there I can't represent $4^ {1 2}$ only using basic operations Is there a way to do that?
  • Fraction exponents in division - Mathematics Stack Exchange
    You can only subtract exponents when bases are same Take for example two numbers 16 and 8 if you divide them, the answer is 2 Numerically, $$\frac {16} {8}=\frac {2^4} {2^3}=2^ {4-3}=2$$ If you even want to imply the above rule in your question, you need log to convert them in the same base and I am unsure if you know log So let it be :)
  • Binomial Theorem for Fractional Powers - Mathematics Stack Exchange
    You know that this extension makes you cross the boundary between algebra (without topology) to analysis (with topology creeping into the scene) just because binomial theorem with, for example, exponent $1 3$ means expanding $ (1+x)^ {1 3}=1+ (1 3)x+ $ into a series, and there are convergence issues for the proof (radius of convergence= ?) With a pseudo like yours, this should sound clear
  • How do you simplify fractions that have exponents?
    To simplify a fraction with powers in the numerator and denominator a possible method is to factor each power base into prime factors With practice it can be done directly if the bases are small numbers $2$ and $3 $ are prime numbers
  • Simplify with fractional exponents and negative exponents
    Simplify with fractional exponents and negative exponents Ask Question Asked 12 years, 10 months ago Modified 11 years, 4 months ago
  • algebra precalculus - What are the Laws of Rational Exponents . . .
    All of the properties of exponents that we learned for integer exponents also hold for rational exponents " So what exactly are the restrictions on the Laws of Exponents in the real-number context, with rational exponents?
  • exponentiation - Calculating Irrational and Fractional Powers of a . . .
    We can write $3^ {0 6}$ as $3^\frac6 {10}$ and can be simplified to $3^\frac3 {5}$, yet it is tedious to calculate by hand, as well as $3^e$ and $3^ {\pi}$? How can I do this without calculator? Like h
  • Calculating logs and fractional exponents by hand
    Before computers were available log tables were used to compute logs and fractional exponents You say "by hand" but I'm assuming that reasonably sized pre-computed tables are allowed
  • Understanding fractional exponents - Mathematics Stack Exchange
    Understanding fractional exponents Ask Question Asked 7 years, 7 months ago Modified 7 years, 7 months ago





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