# Algebra Feedback

by Ron Kurtus

Readers have sent in a total of **70** comments and questions on Algebra issues. They are listed according to date.

You can read them to further your understanding of the subject.

## List of most recent 15 letters

## Title |
## Topic |
## Country |

Special exponent cases |
Exponents |
Cameroon |

Puzzle question |
Product of Two Negative Numbers is Positive |
India |

Product of Two Negative Numbers |
Product of Two Negative Numbers is Positive |
India |

Solving single variable equations |
General |
India |

Multiply terms with different base |
Multiplication with Exponents |
USA |

Raise number to the zero power |
Division with Exponents |
Canada |

Solving a problem |
Variables and Constants |
USA |

Why are letters used in equations? |
Purpose |
Nigeria |

Formula without constant and variable |
Variables and Constants |
UAE |

Is zero a variable? |
Variables and Constants |
India |

5^6 times 8^6 |
Multiplication with Exponents |
USA |

Where did naming conventions come from? |
Variables and Constants |
Australia |

Is number 4 is variable term? |
Variables and Constants |
India |

What is a value? |
Variables and Constants |
USA |

Suggested algebra resource |
Resources |
USA |

### Exponents

## Special exponent cases

February 24, 2020

### Question

Thank you sir for the opportunity to ask a question.my question goes like this:

we talk of a^m ×b^m = (axb)^m , and a^m × a^n = a^(mn); But if we have:

Q1. a^m × b^n = ??, And

Q2. 16a^5 ÷ 4a^2 = ???

Please help on what to do in these cases since no law backs them.

Kwo - **Cameroon** (29367)

### Answer

Often it is handy to write the problem with small numbers to understand the rule.

Note that a^m × a^n is not = a^(mn). Consider a^2 x a^3 = aa x aaa = a^5 = a^(2+3) or a^(m+n)

Q1: Even using small numbers, you can see the a^m x b^n cannot be simplified.

Q2: 16a^5 ÷ 4a^2 = (4^2*a^5)/(4a^2) = 4a^(5 - 2) = 4a^3

I hope that helps. Best wishes for success in Algebra.

### Product of Two Negative Numbers is Positive

## Puzzle question

January 1, 2019

### Question

which is that eight digit grid whose three cosecutive numbers is even number and whose sum is nineteen

Note:-there is digit 6 at eighth place when we move from right to left and also digit 6 at seventh place when we move from left to right

Bashir ahmad - **India** (28902)

### Answer

That problem seems like quite a puzzle. I am sorry but I do not have the solution to this problem.

Best wishes in finding a solution.

### Product of Two Negative Numbers is Positive

## Product of Two Negative Numbers

May 5, 2018

### Question

why we take x= ab+(-a)(b)+(-a)(-b)=ab

because (-a)(-b)is already a question to proof

MANISH - **India** (28544)

### Answer

(-a)(b) = -ab

(-a)(-b) = +ab

ab + (-ab) = 0

Thus ab+(-a)(b)+(-a)(-b)= ab

### General

## Solving single variable equations

March 31, 2018

### Question

If k is constant can we find solutions to single variable equations

Vidi - **India** (28493)

### Answer

"k" will be involved in solutions to the equations. See: Solving an Algebraic Linear Equation with One Variable for information.

### Multiplication with Exponents

## Multiply terms with different base

November 3, 2017

### Question

I need to find out how to multiply terms with different base and exponents but i looked online and nothing shows up something like this. XY* in a radical multiplied by x*y to the third power inside a radical. Please help it feels hopeless right now

Lester - **USA** (28307)

### Answer

I'm not sure I understand what you are trying to do. Are you trying to multiply something like (2^3)(5^2)?

### Division with Exponents

## Raise number to the zero power

October 16, 2017

### Question

(3x^-3)^0

Does the exponent -3 x 0 = 0?

Jonathan - **Canada** (28290)

### Answer

Any number raised to the zero power equals 1. For example x^0 = 1.

Thus (3x^-3)^0 = 1

### Variables and Constants

## Solving a problem

March 28, 2017

### Question

kindly solve for me an algebra problem that is similar to the problem below and give me a step by step procedures:

b=ka+3, k is a constant, if the possible solutions are in the forms (a, b) is (2,3) a solution to the equation?

moifee - **USA** (27967)

### Answer

What are you trying to find a solution for? a, b, or k?

If a = 2 and b = 3, then 3 = 2k + 3, and k = 0. But I don't think that is what you are looking for.

### Purpose

## Why are letters used in equations?

March 11, 2017

### Question

why did they choose to use letter of alphabets or other symbols as a subject of the formular when numbers can still serve and is even easier to be used in rounding up calculation?

Chidi - **Nigeria** (27935)

### Answer

Numbers are used in specific cases. The letters of the alphabet are considered variables, such that the equation or formula can be used with any numbers.

See Variables and Constants in Algebra for an explanation.

### Variables and Constants

## Formula without constant and variable

March 1, 2017

### Question

Using formula without constant and Variable is right or wrong.(4-9/2)square 2 please clear it.thanks

Jamil - **UAE** (27918)

### Answer

Just having numbers in the expression is simply an arithmetic exercise. What you have written is (4 - 9/2)^2, which would be (-1/2)^2 = 1/4.

### Variables and Constants

## Is zero a variable?

February 13, 2017

### Question

0 is variable or constant

Chandra - **India** (27877)

### Answer

Since zero (0) does not change, it is a constant and part of the number system.

### Multiplication with Exponents

## 5^6 times 8^6

January 31, 2017

### Question

hi, i have a question that is 5 to the 6th power times, 8 to the 6th power... how do i do this i asked everyone and they don't know how

thank you

noelle - **USA** (27847)

### Answer

5^6 (5 to the 6th power) times 8^6 = 40^6 (40 to the 6th power).

(5^6)*(8^6) = (5*5*5*5*5*5)*(8*8*8*8*8*8) = 40*40*40*40*40*40 = 40^6

In general, (x^a)*(y^a) = (xy)^a

### Variables and Constants

## Where did naming conventions come from?

August 9, 2016

### Question

Ron - from this abc usually constants and xyz variables, but any idea why linear algebra use ith and jth for row and column and then refers to a 2x3 matrix as an mxn matrix. Was wondering if ijkmn arent used so much - or could it be m for myrian and n for numberth nth - even non maths people know what to the nth degreee means? But I is often used for interest as is r for rate. K is most often a specific constant. n I can understand to the last n number but m has me stuck - unless it is like a-z m to n?

TIMOTHY - **Australia** (27199)

### Answer

That is a puzzler. I haven't been able to find where the conventions for naming constants, variables, table rows and columns, and nth degree come from.

There must be some rationale hidden in the archives of mathematical history.

If you ever find out, let me know.

### Variables and Constants

## Is number 4 is variable term?

April 27, 2016

### Question

1. Is number 4 is variable term? If yes, how?

2. Are all constants are variables? if yes, how?

srilata - **India** (26968)

### Answer

The number 4 is a constant value. "Constant" means the item does not vary. "Variable" means that it can change. Usually, variables are designated by letters.

### Variables and Constants

## What is a value?

April 17, 2016

### Question

Hi:

I have a question which constantly troubles me.

what is a value ? I found many definitions for the term "value" in Math., i.e. the number represented by a symbol(which is called variable); number represented by a figure, symbol or alike; results of a function or calculation; a particular number; the magnitude(size or amount) of a number; an assigned or calculated numerical quantity (i.e. 3m/sec); etc.

So, what does "value" mean in engineering when we say a physical quantity(i.e. the pressure of the gas) assumes a set of values and when you say" a fixed or constant value of k = 1.38*10-23" ? Here, I think we mean " assigned or calculated numerical quantity" or "number represented by a figure ". We are not talking about numbers assigned to letters (variables in algebra) here, right ? Given many definitions of the term "value" in the math and engineering, I got confused what it means when it appears in a sentence.

Please help me to clear my mind and resolve the confusion I have had for a long time. If my question is not clear, please let me know.

Thanks,

Wei - **USA** (26938)

### Answer

Some of these terms can be confusion, either because they are carelessly used or are different in other disciples.

If you have an Algebraic symbol that can vary, it is called a variable. Otherwise it is a constant. In either case, you can assign a number or value to it, such as a = 5.

But note that the Algebraic symbol can represent a physical entity, like is used in engineering. But typically, values in engineering or physics have units attached to them, such as a = 5 m/s.

Looking at examples and applications is probably the best way to get a feel for the definition.

I hope this helps.

### Resources

## Suggested algebra resource

March 2, 2016

### Question

Hello,

I just want to say that I'm loving math and like to help people to learn it.

I know that many people struggle with Algebra, so I created some calculators to help students.

You can check them out here at: http://www.emathhelp.net/calculators/other/math-problem-solver/

Might be worth adding to the site or recommending to students.

Either way, have a great day!

Best wishes,

Paul - **USA** (26830)

### Answer

Thanks for the resource. I added your page with all calculators at Algebra Resources page.

Best wishes in your activities.

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