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The exponent $0$ provides $0$ power (i.e. gives no power of transformation), so $3^0$ gives no power of transformation to the number $1$, so $3^0=1$. Once you have the intuitive understanding, you can use the simple rules with confidence.
- The Shape of Mathematical Self-Tutelage
I am interested primarily in physics, and I am generally...
- The Shape of Mathematical Self-Tutelage
28 lip 2023 · If we start only with \(a^1=a\) and the product rule, then we can immediately prove that \(a^0=1\) because \(a^0\cdot a=a^0\cdot a^1=a^{0+1}=a^1=a\), and dividing through by a (which is assumed not to be zero), we conclude that \(a^0=1\). But then for any positive integer n, $$a^n=a^{\overset{n\text{ times}}{\overbrace{1+1+\cdots+1}}}=\overset ...
6 cze 2021 · 😉 In this exponents tutorial I explain why any number to the power of 0 (zero power) always equals 1. I provide Illustrations that explain the zero exponent rule. I also explain what a...
18 lut 2016 · But what about the zero power? Why is any non-zero number raised to the power of zero equal 1? And what happens when we raise zero to the zero power? Is it still 1?
The definition $\ 2^0 = 1\ $ is "natural" since it makes the arithmetic of exponents have the same structure as $\mathbb N$ (or $\mathbb Z\:$ if you extend to negative exponents).
31 sty 2017 · So, it is logical to continue dividing by two,and reach the conclusion that $2^0$ = 1. This is true for negative powers, and is so because it is the most logical way to define powers outside of the natural numbers.
Answer: As already explained, the answer to (-1)0 is 1 since we are raising the number -1 (negative 1) to the power zero. However, in the case of -10, the negative sign does not signify the number negative one, but instead signifies the opposite number of what follows.
