# exponent

1. ### negative sign under radical

Hi, So I'm hoping someone can clarify for me why it is possible to take out the negative sign that is under the radical (in the image attached)? I thought this was only possible if the exponent which the number was raised to was odd. e.g. I thought that (-27)^(1/3) = -(27)^(1/3) is allowed, but...
2. ### Creating exponential equations

Hello, I have the two equations: h(x) = 3(3)^x f(x) = 100(2)^(x/32) h(x) is the number of people told during the hour, x, and x = 0, corresponds to the hour which the first 3 people heard the rumour and started telling others. f(x) is the total number of bacteria within a culture which...
3. ### Use of Calculus

What is the use of calculus in computer engineering. we study math in computer like boolean algebra,general math for programming but what computer does with calculus?(Clapping)
4. ### Exponents and negative numbers - think I'm missing something

If -2*-2*-2*-2= 16 Why does -2 to the fourth power =-16? I'm sure I'm just missing some rule or I'm unclear on a definition of something. If some one could set me straight id sure appreciate it.
5. ### Implicit Differentiation

y^2 = e^(xy) y' = ye^(xy) / [ 2y - xe^(xy) ] Is it wrong if my final answer written Like this? y = sqrt[ e^(xy) ] y' = ( sqrt[ e^(xy) ] )e^(xy) / [ 2( sqrt[ e^(xy) ] ) - xe^(xy) ]
6. ### Need help solving for part of fractional exponent

Want to solve for x in equation: y =a^(1/x). Unable to isolate x on left side of equation so get equal values on both sides when replacing y & a with numbers. This is the orig equation with numbers: 0.01 = 0.67^(1/x) Thanks for any help.
7. ### Exponent Rules - where can I find out more?

Hi all, Are these rules for exponents valid? I have not come across them previously and would love to know more!! $\left[\left(\frac{a}{b}\right)^x+\left(\frac{a}{b}\right)^x\right]^y = a^{xy}\left[\left(\frac{1}{b}\right)^x+\left(\frac{1}{b}\right)^x\right]^y$...
8. ### Rearranging Equations with Exponents

Hi, I've always considered myself fairly good with maths however it's been a few years and I'm obviously rusty. I have an equation with an exponent that I would like to rearrange, however the placing of the exponent on the other side is confusing me. The equation (fairly simple) is as follows...
9. ### Fraction with exponent

If there is a parentheses around a fraction and an exponent is outside do you multiply the entire problem?
10. ### solving for exponent

Pax= Qbx I need to solve for x in terms of P, a, Q, and b. I guess I'm not sure where to begin. Would it help to move everything to one side under one x exponent? (1 = (Pa/Qb)x? And then the answer would be 1/log(Pa/Qb)? Or do I need to use a logarithm first? x log(Pa) = x log(Qb) ... but...
11. ### need help with sine exponent

I'm reviewing my calculus lessons and notice there is a question with sin^3*x and it asks for the derivative. First of all though, I'm not sure how to plug sin^3 into a calculator since it usually asks for sin(something in here) so would sin^3 also equal sin(x)^3? and would the derivative then...
12. ### binomial formula when the exponent is negative

Hi; Can someone give me the formula for binomial expansion when the exponent is negative / or a fraction? I know the expansion I just need the formula. Thanks.
13. ### How to solve an equation with a variable as exponent set equal to a polymonial

I want to know if anyone can help me to solve this equation: 6x = 24x2 I don't know how to handle the right side of the equation. I start this way: 6x = 6(4)x2 6(x-1)= 4x2 But I wasn't sure how to proceed. I think logarithms must be involved, but I am not sure how to apply...
14. ### Finding result of calc with upto 14 digits exponent

I want to know if I have 123 (base) ^ (raised to power) 14 digits exponent number, how can i do it? Currently mathematica is supporting only 9 digits in raised to power but i need calculation for raise to power 14. Is there any method or trick available to calculte such big calculation? If...
15. ### Simplify Rational Exponent

I understand that (16)^1/3 = cuberoot(16). How do I change the cuberoot(16) to be 2*cuberoot(2)?
16. ### Exponent question?

Hello, I'm new to the forum and English isn't my first language, so I'm sorry for my mistakes. The expression (0,02)^2 is equal to: A) 5^40 B) 5^-40 C) 25^40 D) 25^-40 E) 2^200
17. ### Sequence Problem with Exponent - # 2

a_{n} = (\dfrac{n + 1}{n - 1})^{n} Converge to what value, or diverge? The answer is e^{2} \lim n \to \infty [(\dfrac{n + 1}{n - 1})^{n}] = indeterminate \ln[(\dfrac{n + 1}{n - 1})^{n}] n \ln[(\dfrac{n + 1}{n - 1})] Next step?
18. ### Sequence Problem with Exponent

I know the limit as n goes to infinity of 8^{1/n} = 1, but what about (0.03)^{1/n} ??
19. ### Finding the derivative of a polynomial with an exponent

"Let . Then, " I don't know where to start here. I want to use the product rule, but I'm not totally sure what to do with the outside exponents.
20. ### Exponent Problem

5x^{-2} = \dfrac{1}{5x^{2}} However \dfrac{5x \ln(x)}{x^{3}} \neq \dfrac{\ln(x)}{5x^{2}} \dfrac{5x \ln(x)}{x^{3}} = \dfrac{5\ln(x)}{x^{2}} ???