choose one rule that applies to exponents, explain how the rule works, and provide an example for your classmates to solve.

Question

choose one rule that applies to exponents, explain how the rule works, and provide an example for your classmates to solve.

Answer 1

Another exponent rule is when you have a base number raised to a negative power or exponent. The expression is written as x^-5.  Just like a positive exponent means multiplying the base n number of times, the negative exponent means to divide because the opposite of multiplying is dividing. So x^-5 =1/x⁵ . In other words, any nonzero number raised to a negative power equals its reciprocal raised to the opposite positive power.

Answer 2

Wow! I wish I could have one of my students supply you this answer instead of me because she just proved most of the exponent rules in today's lesson!

The rules really build on each other so it doesn't get fun until you've proven a few different ones. Let's walk through the most basic one and get you started on a more fun one and see where you take it! 

a^ba^c = ?  

The exponent tells us how many times we multiply 'a' by itself.

/--  b times--\ /----c times----\

(aaa..........a)·(aaa..............a)   => Well that's 'a' times itself b+c times

a^ba^c = a^b+c

So try this one!

(a^b)^c = ?   You can prompt your classmates at each of the following steps.

1. Rewrite this using the basic definition of exponents.

Hint: Treat the (a^b) part as the 'thing' being multiplied 'c' times.

2. Use the rule we just proved above to rewrite the expression again.

3. Apply the definition of multiplication (repeated addition) to the exponent to rewrite one more time.

Result: You should have just proved that (a^b)^c = a^bc   The power rule!

Plug in your favorite numbers as an example for the class to solve. (I'd avoid negatives for 'b' and 'c' just yet.)

 

 

Answer 3

x^m × xⁿ=x^m+N

ex:  2²×2³=2²⁺³

             =2⁵ =32  (R.H.S)

L.H.S: 2²=4,  2³=8

  =2²×2³=4×8=32

L.H.S =R.H.S