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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.

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What is this equation formally?

Having fun with the calculator, I realized that : (a^c) and (a^b) with c > b and c > 4 and b = 2 a^c / a^b = a^(c-2) So, for example: 3^5 / 3^2 = 27 is same that 3^(5-2) => 27 I know it's basic, but how is this happening? What is this formally…
ESCM
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Reducing An Exponent

I am reading a science book in which the author claims there are $4^{100}$ different combinations of amino acid sequences in a gene that has a length of $100$ amino acids. No need to worry about the science here. My main concern is in the next…
Jim Stewart
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Weird sum of exponentials

Is there a way to solve this: $$3^x + 4^x + 5^x = 6^x? $$ I used brute force for this, but I dunno the solution. Any idea would be a great help. :)
rosa
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What is zero to the power of zero? $0^0$

Evaluate: $$0^0$$ Would you use this law of indices? $$x^0=1$$ Or would you use that: $$\frac{x^n}{x^n}=x^0$$ which would mean $$\frac{0}{0}=undefined$$
Xetrov
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Reciprocal of 9's

I happened upon an interesting pattern today. If I take the reciprocal of $998$, I get $.001002004008016032064128\dots$ which has a pattern of powers of $2$. If I take the reciprocal of $997$, I get a pattern with powers of $3$,…
esteuart
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How do we accurately define a negative raised to a fractional power, as it can be written in different ways which is misleading

Negative to fractional (and decimal) power can be misleading : For example: $(-2)^{2.1}$ may be expressed as: $(-2)^{(21/10)}$ = $\sqrt[10]{(-2)^{21}}$ = $\sqrt[10]{\text{negative}}$ = $\text{a complex number}$ OR: $(-2)^{(210/100)}$, which is same…
anonymous
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Can you explain why $(\sqrt{n})^3 = \sqrt{n^3}$?

That this, why does, for example, the square root of $n$, cubed, give the same value as the square root of $n$ cubed?
s.xw
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Exponents (Indices) grade 6-7 worded problem

I am a a student and I am having difficulty with answering this question. Please may I have a step by step solution to this question so that I won't have difficulties with answering these type of questions in the future. A car travels at at a speed…
OliviaAages
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Finding remainders.

I just incurred a question which asked me to find the remainder when $41^{77}$ is divided by $7$. I just saw $41$ and then the number $6$ striked to me as $41-35=6$. I chose $35$ as it was nearest to $41$ but I think the way I solved it is wrong.…
Mayank Mittal
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Simplifying indices

I have the question : simplify $$\frac{X^{1/3} \cdot X^{4/3}}{X^{-1/3}}.$$ So I have simplified as much as I could and got $$\frac{\sqrt[3] X \cdot \sqrt[3]{X^4}}{1/\sqrt[3] X}.$$ However the solutions says that the final answer should be $X^2$.
Dan
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$5^a = 3^b = 225^c$ where $a \not= b \not = c \not = a$ . Find the relationship between $a , b$ and $c$

One of the solutions to the above equation would be where $a, b$ and $c$ are equal to 0 , but there is a condition that says neither of those variables are equal to each other. I have a feeling the question is wrong . The answer given at the back of…
Sushruta Nandy
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Question on Indices and specifically solving for an indice that has the value "x"

Trying to workout 3(3$^x$) = 27$^{2x}$ So far i have done the following, 3(3$^x$)= 27$^{2x}$ (3)(3$^x$) = 27$^{2x}$ (3)+$x$= (9$^x$)(3$^x$) Cant see what to do next... Thanks for any help!
John Allen
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Help in solving exponential equation

Solve the following equation: $$\frac{8^x + 27^x}{12^x + 18^x} = \frac{7}{6}$$ All I managed to do is rewrite the given equation in a simpler form: $$\frac{4^x}{6^x + 9^x} + \frac{9^x}{6^x + 4^x} = \frac{7}{6}$$ I don't know what should be done…
George R.
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Does $a^nb^n=(ab)^n$ apply to $c^m(x-x_0)^m$?

Does the power of a product rule $$a^nb^n=(ab)^n, a,b \in \mathbb{R}, n \in \mathbb{N}$$ apply to $$c^m(x-x_0)^m, c,x, x_0 \in \mathbb{R}, m \in \mathbb{N}$$ so that $$c^m(x-x_0)^m=(cx-cx_0)^m$$ ?
mavavilj
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Find the value of the constants

If $\displaystyle \frac{\left( \frac{2x^2}{3a} \right)^{n-1}} {\left( \frac{3x}{a} \right)^{n+1}} = \left( \frac{x}{4} \right)^3$, determine the values of the constants $a$ and $n$ I could find the value of $a$, i.e, $\displaystyle…
Nikitha Govula
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