Question

How to math with crispy rat
Exponents go brr

Answer 1

The Basics:
How does an exponent work? Well lets see: Say you have \(x^y\). The x is the constant and the y is the exponent. This means that the x is repeated y times, For example, if I had \(3^2\) we would multiply \(3\) by \(2\) times which is the same as \(3\)*\(3\)=\(9\).
Also anything to a negative power is the same as the reciprocal of the positive power. And a negative to the power of a positive odd exponent is negative while for a positive even is a positive number.
Note: An exponent is not the same as regular multiplying. \(3^3\)=\(3\)*\(3\)*\(3\) NOT \(3\)*\(3\)=\(9\).

Answer 2

Simplifying a number to be an exponent:
To simplify an exponent you have to simplify the number to the point where each factor is a prime number. Then we want to see how many times the factors are repeated and have it as the form of \(x^y\). Assuming x=factor and y=number of times repeated
For example:
\(32\)=\(2*2*2*2*2*2\) In this case \(2\) is repeated \(6\) times. So it is \(2^6\). If two factors have the same y value you can multiply them together.

Answer 3

Dividing exponents with the same base:
If two exponents have the same constant/base and you’re dividing then you can make it equal to \(a^b\)/\(a^c\)=\(a^b-^c\).
Lets see why this works with an example,
First let’s expand \(4^2\)\(4^1\)-->\(4*4\)/\(4\) if you know about division then you would know that upi can cancel out the same number of 4’s on the bottom and top. And you get \(4\)\\(1\)=\(4\) which is the same as \(4^2\)/\(4^1\)=\(4^2-^1\)=\(4^1\).

Multiplying exponents with the same base:
If two exponents have the same constant/base and you’re dividing then you can make it equal to \(a^b\)/\(a^c\)=\(a^b+^c\)
Let’s see why this works with an example:
First let’s open up \(4^2\)*\(4^1\)=\(4*4*4\) Using the paragraph earlier on simplifying numbers we would get \(4^3\) because \(4\) repeats \(3\) times.

Answer 4

Let's say you don't have the same base what would you do:
First determine what is the base you want.
Next rewrite the base of your number as the most simplified form bit don’t group it
Then group the necessary parts into exponents form so that you can get the desired base
Finally, multiply the current exponent along with the ones you just formed.

For example:
I have \(4^2\) but i want it the base to be 2
Break it down into
\((2*2)^2\)=\((2^2)^2\)=\(2^(2+2)\)=\(2^4\)

Answer 5

NOTE:
Anything to the zero power is 1 but zero to the power of anything is 0.
I did not cover everything or may have covered something poorly as those may be a bot hard to explain feel free to read here:
https://www.rapidtables.com/math/number/exponent.html
https://www.prodigygame.com/main-en/blog/exponent-rules/
https://www.mathsisfun.com/algebra/exponent-laws.html
https://www.youtube.com/watch?v=XtY8acpPUag&t=142s

Answer 6

Calculator:
https://www.calculatorsoup.com/calculators/algebra/exponent.php

Answer 7

since we are into exponents here are the rules to follow when you have to do with some exponents equations:
\[ \begin{array}{ll}
1^{a}=1 & a^{1}=a \\ \\
a^{0}=1, a \neq 0 & 0^{a}=0, a \neq 0 \\ \\
(a b)^{n}=a^{n} b^{n} & a^{b+c}=a^{b} a^{c} \\ \\
\left(a^{b}\right)^{c}=a^{b \cdot c} & a^{c} \cdot b^{c}=(a \cdot b)^{c} \\ \\
\frac{a^{m}}{a^{n}}=\frac{1}{a^{n-m}} \text{ when} ~n>m \ \ \ \ \ & \frac{a^{m}}{a^{n}}=a^{m-n} \text{ when } m>n \\
\end{array} \]
here are a couple of equations you might try to solve - giving answers as well so you can check if you are correct:
\[ \frac{16^{-x}\times \:4^{4x}}{8^3}=32 \ \ \ \ \ \ \ \text{answer: } x=\frac{7}{2} \]
\[ \left(2^2\right)^x\times 2^{3x}=32 \ \ \ \ \ \ \ \text{answer: } x=1 \]
\[ \left(\frac{3^{7x}\times \:3^{5x}}{3^{8x}}\right)=81 \ \ \ \ \ \text{answer: } x=1 \]
\[ \frac{9^{2x}\times \left(3^x\right)^2}{27\times 3^{4x}}=\frac{1}{9} \ \ \ \ \ \ \ \ \text{answer: } x= \frac{1}{2} \]
this is to try YOUR skills, not some website's math bot skills :D

Answer 8

I was never good in math so thank u

Answer 9

Im not good at math :(

Answer 10

im showing this to my math teacher XD

Answer 11

I'm not that good at math]

Answer 12

wait this was over 10 days ago shoot nvm o_o

Answer 13

this helped thanks alot (3yrs late) 0-0

Answer 14

Thank You for breaking the problem down and showing step by step on how to alone the problems.

Answer 15

BROO I NEEDED THIS SMM THANK YOUU

Answer 16

lets see how my math teacher reacts to this....lol