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Example Questions
Example Question #1 :Exponents
Ifa2= 35 andb2= 52 thena4+b6= ?
141,833
3929
150,000
140,608
522
141,833
a4=a2*a2andb6=b2*b2*b2
Thereforea4+b6= 35 * 35 + 52 * 52 * 52 = 1,225 + 140,608 = 141,833
Example Question #1 :Exponents
If, what is the value of?
Since we have two’s inwe will need to combine the two terms.
Forthis can be rewritten as
So we have.
Or
Divide this by:
Thusor
*Hint: If you are really unsure, you could have plugged in the numbers and found that the first choice worked in the equation.
Example Question #1 :How To Add Exponents
Solve for x.
23+ 2x+1= 72
5
6
3
7
4
5
The answer is 5.
8 + 2x+1= 72
2x+1= 64
2x+1= 26
x + 1 = 6
x = 5
Example Question #481 :Algebra
Which of the following is eqivalent to 5b– 5(b–1)– 5(b–1)– 5(b–1)– 5(b–1)– 5(b–1), wherebis a constant?
1
5
1/5
0
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 51and then apply this rule.
5b– (5(b–1))(5) = 5b– (5(b–1))(51) = 5b– 5(b–1+1)
Now, we will simplify the exponentb– 1 + 1 and write it as simplyb.
5b– 5(b–1+1)= 5b– 5b= 0
The answer is 0.
Example Question #1 :Exponents
If, then what doesequal?
Example Question #1 :How To Add Exponents
Simplify. All exponents must be positive.
Step 1:
Step 2:
Step 3: (Correct Answer):
Example Question #2 :Exponential Operations
Simplify. All exponents must be positive.
Step 1:
Step 2:
Step 3:
Example Question #7 :How To Add Exponents
Answer must be with positive exponents only.
Step 1:
Step 2: The above is equal to
Example Question #1 :How To Add Exponents
Evaluate:
Example Question #1 :How To Add Exponents
Simplify:
Similarly
So
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