Questions tagged [exponentiation]

Questions about exponentiation, the operation of raising a base $b$ to an exponent $a$ to give $b^a$.

Exponentiation is a mathematical operation which produces a power $a^n$ from a base $a$ and an exponent $n$. The objects involved are usually numbers, but the procedure can be generalized to matrices, elements in algebraic structures, sets, etc.

4326 questions

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How do I solve for $t$ and $s$ in $y = x^{-t/s}$?

I have $$y = x^{-t/s}$$ How do I solve for $t$ and $s$ in terms of the other variables?

exponentiation

asked Dec 12 '13 at 22:45

Squirrl

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Why does $2^{-x}$ equal $0.5^x$?

My son mistaken to answer his math question: $2^{-x} = 0.5^{x}$ He said this must be false, I asked ChatGpt but still not satisfied with the answer because I want to explain to my son at age 12. The strange part is: when you look at $2^{-x}$ the…

exponentiation

asked Jan 22 '24 at 22:34

Akam

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How to use exponential decay to determine study time?

From wikipedia: """In 1885, Hermann Ebbinghaus discovered the exponential nature of forgetting. The following formula can roughly describe it: $R = e^{-t/s}$ where $R$ is memory retention, $S$ is the relative strength of memory, and $t$ is time.""" …

exponentiation

asked Jun 20 '11 at 02:53

sf2k

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Why does any non-zero expression raised to the power of 0 equal 1?

How would you answer? When I opened Photomath, it said any non-zero expression raised to the power of zero equals one.

exponentiation

asked Apr 24 '21 at 10:51

MILO PADILLA

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Why does zero raised to any positive power equal zero?

What if you raised 0 to the power of 2?

exponentiation

asked Apr 18 '21 at 03:24

MILO PADILLA

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Simplifying exponents..

Use the properties of rational exponents to simplify the expression $(3^\frac{1}3 \cdot 4^\frac{1}{4})^3$ I got $3^1 \cdot 4^\frac{3}{4}$ I just wasn't sure if this was the most simplified expression. It says to do it without a calculator so can…

exponentiation

asked Feb 04 '21 at 13:39

QuantumPi

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Why Does $a^0 = 1$ and $a^{-p} = {\frac{1}{a^p}}$ if $(a \not = 0) , p \not= 0$?

Why does $a^0 = 1$ and $a^{-p} = {\frac{1}{a^p}}$ if $(a \not = 0)$ and $p \not= 0$? How can we prove these formulas?

exponentiation

asked Jul 02 '19 at 02:34

244boy

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Can someone explain this inequality transformation

I have seen this transformation but am not sure what laws are applied to achieve it. $$ \frac{1}{2^{n+1}} \leq 10^{-6} \Rightarrow2^{n+1} \geq 10^6. $$ I feel it is related to $x^{-1} = \frac{1}{x}$ and hence removing the negative exponents from…

exponentiation

asked May 21 '18 at 18:27

clicky

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Get $n$ where $x = 10^n$

Say we have $x = 10^n$. Is there a way to simplify/change this equation to isolate $n$, e.g. represent $n$ as a function of $x$? Just too add a few lines and not get this question posponed, please represet the answer as "$n = \dots$"

exponentiation

asked Sep 24 '16 at 17:12

x - 1

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Is there a formula or an algorithm to find the power of any integer that returns zero?

Is there a formula or algorithm that can find the power ${^x}$ that returns $0$ for $n$ ${\mathbb N} $?

exponentiation

asked Aug 18 '16 at 10:08

ctrl-alt-delete

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The 'unique' way powers are calculated

everyone. My question for you is why a power, such as m^n^o is calculated as m^(n^o), and not (m^n)^o. Let me explain why I don't fully understand this: As we know, we are supposed to perform calculations from left to right, starting with brackets,…

exponentiation

asked Apr 01 '16 at 03:05