Need help with a math problem ASAP! Thanks!!

Question

1. What repeated mathematical operation is represented using exponents? Create an example as part of your explanation. (10 points)

2. Why is it that when you have a power to a power situation, why do you multiply the exponents? Create an example as part of your explanation. (10 points)

3. Explain the steps that you would use to simplify the power expression shown.

Answer 1

Using exponents represents the repeated use of multiplication on a single number, the base, for a given number of times

2³ = 2x2x2

By the same reasoning, when a power is raised to another power you repeatedly multiply that power on the base for the given number of times. You follow with the applicable rules YOU ADD the exponents

A longer version of the above is

(2³)² = (2x2x2)x(2x2x2) = 2^3x2 = 2⁶

A slightly shorter version

(2³)² = 2³ x 2³ = 2³⁺³ = 2^3x2 = 2⁶

Also you want to keep in mind the relationship between multiplication and addition. Multiplication is a faster way of adding the same number for a given number of times and the multiplication table you learned long ago is an illustration of just that.

For your problem note that 4 is 2²

(2³ • 3⁴)/(4 • 3⁵)

Can be rewritten as

(2•2•2)(3•3•3•3)/(2•2)(3•3•3•3•3)

Next Cancel out common quantities between the numerator and denominator of your fraction

Two of the 2s cancel out and 4 of the 3s cancel out and you are left with

2/3

I hope this helps

You can also look up the definition of an Exponent and the rules for using them if you want more detail. Where you will find the rules for dividing Exponents and this can be used just as well to simplify your problem, give it a try. (2^3-2)•(3^4-5) is also 2/3.