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Example Question #2 : How To Add Exponents
Which of the following is eqivalent to 5b – 5(b–1) – 5(b–1) – 5(b–1) – 5(b–1) – 5(b–1) , where b is a constant?
0
1/5
5
1
5b–1
0
We want to simplify 5b – 5(b–1) – 5(b–1) – 5(b–1) – 5(b–1) – 5(b–1) .
Notice that we can collect the –5(b–1) terms, because they are like terms. There are 5 of them, so that means we can write –5(b–1) – 5(b–1) – 5(b–1) – 5(b–1) – 5(b–1) as (–5(b–1))5.
To summarize thus far:
5b – 5(b–1) – 5(b–1) – 5(b–1) – 5(b–1) – 5(b–1) = 5b +(–5(b–1))5
It's important to interpret –5(b–1) as (–1)5(b–1) because the –1 is not raised to the (b – 1) power along with the five. This means we can rewrite the expression as follows:
5b +(–5(b–1))5 = 5b + (–1)(5(b–1))(5) = 5b – (5(b–1))(5)
Notice that 5(b–1) and 5 both have a base of 5. This means we can apply the property of exponents which states that, in general, abac = ab+c. We can rewrite 5 as 51 and then apply this rule.
5b – (5(b–1))(5) = 5b – (5(b–1))(51) = 5b – 5(b–1+1)
Now, we will simplify the exponent b – 1 + 1 and write it as simply b.
5b – 5(b–1+1) = 5b – 5b = 0
The answer is 0.
Example Question #3 : How To Add Exponents
If
Example Question #483 : Algebra
Simplify. All exponents must be positive.
Step 1:
Step 2:
Step 3: (Correct Answer):
Example Question #4 : How To Add Exponents
Simplify. All exponents must be positive.
Step 1:
Step 2:
Step 3:
Example Question #5 : How To Add Exponents
Answer must be with positive exponents only.
Step 1:
Step 2: The above is equal to
Example Question #6 : How To Add Exponents
Evaluate:
Example Question #7 : How To Add Exponents
Simplify:
Similarly
So
Example Question #71 : Exponents
If 
Using exponents, 27 is equal to 33. So, the equation can be rewritten:
34x + 6 = (33)2x
34x + 6 = 36x
When both side of an equation have the same base, the exponents must be equal. Thus:
4x + 6 = 6x
6 = 2x
x = 3
Example Question #81 : Exponents
What is the value of 
We can solve by converting all terms to a base of two. 4, 16, and 32 can all be expressed in terms of 2 to a standard exponent value.
We can rewrite the original equation in these terms.
Simplify exponents.
Finally, combine terms.
From this equation, we can see that 
Example Question #13 : Exponents
How many of the following base ten numbers have a base five representation of exactly four digits?
(A)
(B)
(C)
(D)
Two
Four
One
None
Three
Three
A number in base five has powers of five as its place values; starting at the right, they are
The lowest base five number with four digits would be
The lowest base five number with five digits would be
Therefore, a number that is expressed as a four-digit number in base five must fall in the range
Three of the four numbers - all except 100 - fall in this range.
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