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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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Two hard indices questions, (what is power to a power of fraction) and (how is $(2^x)^2 = 4^x $)

The answer for question 1) is $2^{3b+6}$ Question 2 I only don't get the $Y^2$ bit
Hannah
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How many uranium-238 atoms are left after 1.338 x 10^10 years?

The half-life of uranium-238 is about 4.46 x 10^9 years. How many will there be after 1.338 x 10^10 years? How can I figure this out? I know it's exponential, but how?
ReliableMathBoy
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How to simplify recurrence relation?

I'm having trouble seeing how $$5(2^{n-1} + 5\cdot 3^{n-1}) - 6(2^{n-2} + 5\cdot3^{n-2})$$ simplifies to: $$2^{n-2}\cdot (10 - 6) + 3^{n-2} \cdot (75 - 30)$$ How can I simplify the above expression to get to the second version?
Sean Bollin
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How to see that $2^{n-1} + 2^{n-1} - 1 = 2^n - 1$

How to see that $2^{n-1} + 2^{n-1} - 1 = 2^n - 1$? Is there a rule about adding two powers of the same base I'm not aware of? I know that you can "add the exponents" if you are multiplying numbers of the same base, or "subtract" them if you are…
Sean Bollin
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Besides $2^4$ and $4^2$, are there any other numbers that, with the base and exponent flipped, will equal the same value?

I've noticed that when you flip the base and the exponent in $2^4$ to get $4^2$, you get the same value, $16$. If there are any other numbers that can make this work, let me know. This is just mind-blown for me! Are there any other numbers that…
ReliableMathBoy
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How can this exponential equation be computed

Is there a mathematical way to solve such equations, besides try and error of course? $e^{-x} = 1-x/5$
user -1
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Prove that I can always write a number a, a>0 as any number c, c>0 to the power of some number (a=c^x)

I'm very new to math, I'm sorry if my question is stupid. I started to study math by my own so I can study Computer Engeneering. I'm studying logarithms and I try to come up with simple proofs of the properties I learn as often as possible. In…
Rrmm
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The power of a power

My teacher gets the following: $(x^{2})^{12-k} = x^{2k-24}$ Where I get the following: $(x^{2})^{12-k} = x^{24-2k}$ I'd like to think of $2(12-k)$ as $2*12 - 2*k$ or $-2k + 24$. Why/how am I wrong? He did the following: $x^{4k} * {a^{12-k} \over…
Hum
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Why can't you multiply the exponents when you have addition involved?

For example, $(8^{\frac{1}{3}} + 27^{\frac{1}{3}})^{2}$ why can't you make this $8^{\frac{2}{3}} + 27^{\frac{2}{3}}$? Please explain in a very simple way, thank you :)
Little Black Dog
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Moving an exponent from the top to the bottom of a fraction and vice versa? Help pretty please :)

So I know that $x^{-1} = 1/x$ by definition. yeah okay, why can't you move a variable with an exponent to the top or bottom of a fraction when you have addition or subtraction involved? for example. $$\frac{x^{-3} + 5}{x^8}$$ why can't you make…
Little Black Dog
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Why does 2^-2 equal 1/2^2?

My intuitive way of thinking about it is that it is $2/2/2$ or $2/2^2$, So why then is it $1/2^2$? what is the flaw in my thinking?
Ray Kay
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How do I figure out the value of a number raised to a fractional power?

For example, if I had something like $9^{1\over 2}$, how should I determine how many times I should use the base (the number being raised to the power of the exponent) as a factor? I just need something specific and readable. Should I use a root…
user186302
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Is there a such a thing as a "log root" or perhaps a "power root"?

We all know what a square root is. It's the number that for any $x$, you can calculate $n * n = x$. Is there an equivalent function to determine for any $x$ that you can calculate $n ^ n = x$? How would that work?
corsiKa
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Right way to solve for $\frac{2^{900}*7^{898}}{14^{897}}$

As a sequel to my question How to solve $0.5^{1200}\times (2^{1204})$? : $\frac{2^{900}*7^{898}}{14^{897}}$ Will I first solve the upper raw like did in previous question and then anwser $14^{897}$
Kasperi Koski
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Confusion in "mask bits"

This is the question: By definition of the IEEE754 standard, 32-bit floating point numbers are represented as follows: S (1 bit) E (8 bits) M (23 bits) S: Sign bit E: Exponent M: Mantissa Which of the following is the correct “mask…
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