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Example Questions
Example Question #71 : Exponents
If a2 = 35 and b2 = 52 then a4 + b6 = ?
522
150,000
140,608
3929
141,833
141,833
a4 = a2 * a2 and b6= b2 * b2 * b2
Therefore a4 + b6 = 35 * 35 + 52 * 52 * 52 = 1,225 + 140,608 = 141,833
Example Question #72 : Exponents
Solve for x.
23 + 2x+1 = 72
5
3
7
4
6
5
The answer is 5.
8 + 2x+1 = 72
2x+1 = 64
2x+1 = 26
x + 1 = 6
x = 5
Example Question #1 : 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?
5b–1
0
1/5
5
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 #73 : Exponents
If, then what does equal?
Example Question #5 : How To Add Exponents
Simplify. All exponents must be positive.
Step 1:
Step 2:
Step 3: (Correct Answer):
Example Question #6 : How To Add Exponents
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 #74 : Exponents
Evaluate:
Example Question #9 : How To Add Exponents
Simplify:
Similarly
So
Example Question #75 : Exponents
If , what is the value of ?
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
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