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Hi Carmen, my teacher introduced me to the rules of exponents and I'm totally confused.

No worries, I'll help you understand in no time!

Let's move to the white board.

Let's start with base. The base is the number that gets multiplied. The 4s are the bases.

Ex 1) 4 x 4

Base

The exponent represents the number of times the base is multiplied by itself, in the example the 2 is the exponent

5²

This rule means that when the same bases are multiplied you can add the exponents.

V² x V³ = V⁵

Same thing with dividing! Guess what to do.

V⁹ V⁴ =V⁵

This rule means that when we must multiply the power that is being raised to the power.

(x⁶)³ =X¹⁸

Oh then that means it equals to V⁵!

Hm... since the bases and its division, I must subtract the exponents

That's right! You catch on quick.

So the exponent 6 and 3 being multiplied equals to 18. The final answer is X¹⁸

When the exponent of the base is 0, that means it always equals to 1.

b⁰ = 1

Example:

8⁰=1

Ok so when the base has a negative exponent you do the reciprocal of the base.

b^-a = 1/b^a

^{Example: 32= 1/32= 1/9}

To change from radical notation, you must know the index and exponent of the radicand. In fraction, put them as the exponent of the base which is radicand. The exponent of the radicand is the numerator while the index is the denominator.

n√ a^m= a^m/n

^Example:

7√ a= a^1/7

In order to change from the exponent notation, put the numerator as the index of the radical and the denominator as the exponent of the radicand

a^m/n=n√a^m

Example:

5^5/4=4√5⁵

Since the exponents are the same you can multiply the bases by the same exponent.

Vⁿ x Bⁿ = (V x B)ⁿ

^Example

2² x 3² = ( 2 x 3)²= 36

Since the exponents are the same you can divide the bases by the same exponent.

Example: V⁴ ÷ B⁴ =(V ÷ B)⁴

Ohh so the reciprocal of 3 is 1/3 which means the final answer is 1/9.

Index

Okay so since the index is 7 and the exponent of the radicand is 1, the answer is a^1/7

In this case, the bases are both V so the exponents subtract, meaning 9-4 is 5. The final answer should be V5

Oh so that's why 8⁰=1

I see, so the 4 is the index and the 5 is the base and the other 5 is the exponent.

Wow I learned so much about the rules of exponents. Thank you so much this makes a lot of sense now.