Mathematics Stack Exchange
Mathematics Stack Exchange

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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If $60^a = 3$ and $60^b = 5$, then find $12^{\frac{1-a-b}{2(1-b)}}$

If $60^a = 3$ and $60^b = 5$, then find $12^{\frac{1-a-b}{2(1-b)}}.$ I have included an answer of my own in case you're stuck.
user359548
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Why does $6^7 + 6^8 = 7 \cdot 6^7$, and why does this pattern work for multiple examples (or maybe all)?

Apparently $6^7 + 6^8 = 7 \cdot 6^7$, but I'm not sure why this pattern works. I also just plugged in two other examples, $3^1 + 3^2 = 4 \cdot 3^1$ and $4^2 + 4^3 = 5 \cdot 4^2$, it also works.
maudulus
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What is (a+b)^x called?

I'm wondering what (a+b)^x is called. I will need this information to study for a test, but I could not manage to Google this one out. Specifically, I need to know (a+b)^2 and (a+b)^3 are. While we're on the topic, I'm wondering how you expand the…
user3576467
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Exponents using non integers

Let’s imagine that the number of rabbits in a field doubles each month. If we start with 6 rabbits, how many rabbits would be in the field after 10 weeks, given that 4 weeks = 1 month? I would think the answer would be $$6 * 2^{2.5}$$ which equals a…
S.Kumar
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Is it possible to convert $y = a^x + b^x$ to the form of $y = a \cdot b^x$?

I don't think this is possible, but I wanted to ask people who know more than me. Is it possible to convert $y = a^x + b^x$ to the form of $y = a \cdot b^x$?
Nick James
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Is there an imaginary Exponent with $a^x=-b$ while a,b>0

Is there an imaginary Exponent $x$ with $a^x=-b$ while a,b>0 ? An where could something like this be used?
SAJW
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How to expand and solve using exponent laws and algebra?

How do you solve this question, specifically between lines 2 and 3 in the image? The intuition, expanding and math behind it would be much appreciated! Question needing solved
Sarrob
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How many zeros are at the end?

My answer to the following problem is 1337 (from the first one) +2 (from the second one) + 4646 (from the last one) = 5985. But it is different from what in answer sheet. I wonder whether I get the concept wrong. It is highly appreciated if anyone…
user321527
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How to solve an equation with the unknown variable both in the exponent and in linear summand?

How to solve the following equation? $$e^{dz} - mdz = 1$$ where $z$ is the unknown variable, the others are constants, $\exp(x)$ is taking $e$ to the power $x$ . I am interested in real solutions for m > 1.
Serge Rogatch
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What happens when I increase the exponent and decrease the base?

Let $y_1=r^n$, where $r>1$ and $n>1$. Suppose we decrease $r$ and increase $n$ such that $y_2=(r-\epsilon)^{n+\beta}$. If $\epsilon>\beta$, can we prove that $y_2
acyuzuguler
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Is this equation on exponentiation true?

Is the below equation true for all real values of $a$, $b$, $c$ and $d$? (with $c\neq0$) $$d(a+b)^c= (ad^{1/c}+bd^{1/c})^c$$ Some cases has been tested and the above has not been disproved.
user289661
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Exponential Growth

A bacteria culture is known to grow at a rate proportional to the amount present.After $1$ hour $1000$s stands of the bacteria are observed in the culture;and after $4 $years $3000$ strands. Find: an expression for the approximate number of strands…
emmanuel mensah
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Does $2^{k+1} = 2^k * 2^1$?

I'm not sure how to deal with an exponent like this. Can I simplify it into terms that are easier to work with? I know that $2^3 · 2^4 = 2^{3+4} = 128$, but I don't know about $2^{k + 1}$
123
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SAT question about integers and exponents

If $a$ and $b$ are positive integers and $$(a^\frac{1}{2}\times b^\frac{1}{3})^6=432$$ What is the value of $ab$?
Veo
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Degree of a root term?

I had the textbook question: What is the degree of the following expression: $x^2\sqrt{y-5}$ Would it be 2.5, since it would be the sum of the exponents of $x$ (2) and $y$ (.5, I think)? Or is this wrong? The confusing part is the exponent of $y$,…
Jonathan Lam
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