Match the exponential expression with its rule:

1. a^ma^n a. a^m b^m
2. (ab)^m b. 1
3. (am)^n c. a^mn
4. a^0 d. 1/a^n
5. a^(-n) e. a^m+n
match the numbers with the letters.

We have to match each exponents expressions with its rule.

Given the exponent expressions:

1.

⇒

2.

⇒

3.

⇒

4.

⇒

5.

⇒

Therefore,

Matching of the given expression with its rule are as follow.

1.            → E

2.                 → A

3.         → C

4.                     → B

5.                  → D

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}