(NEED ASAP) Properties of Exponents Assignment

Question

1. 1. What repeated mathematical operation is represented using exponents? Create an example as part of your explanation.
2. 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.
3. 3. Explain the steps that you would use to simplify the power expression shown.

Answer 1

1) multiplication

2)

(B^k)^n

= (B^k) * (B^k) * (B^k) * ...* (B^k) <-- there are N factors of B^k

each of these factors contains K factors of B...

therefore there are k*N factors of B , which is B^(n*k)

3)

2^3 * 3^4 2^3 * 3^4 2^3 3^4

------------- = -------------- = -------- * --------- <--- splits into 2 fractions

4 * 3^5 2^2 * 3^5 2^2 3^5

= 2^(3-2) * 3^(4-5) <-- quotients: SUBTRACTS the exponents

= 2^(1) * 3^(-1)

= 2 * 1/3 <--- property of negative exponents

= 2/3

Answer 2

Exponents represent multiplication, of the base number times itself, the number of times represented by the exponent. Example: 2³ means multiplying the base number (2) times itself three times (2•2•2).

When we have a power raised to a power we are multiplying the base by its self according to the first exponent then, multiplying the results by those results the number of times according to the second exponent. Example (3⁴)⁵ means (3•3•3•3)⁵ = [(3•3•3•3)(3•3•3•3)(3•3•3•3)(3•3•3•3)(3•3•3•3)] = 3²⁰ = 3^4•5

There are lots of ways of simplifying the expression

One way would be to write 4 as 2² then to subtract the exponents of the "2"s and then again subtract the exponents of the "3"s like this:

The results would be 2¹•3^-1 = 2•1/3 = 2/3