# PSAT Math : Exponential Operations

## Example Questions

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### Example Question #1 : How To Add Exponents

If a2 = 35 and b2 = 52 then a4 + b6 = ?

141,833

522

150,000

3929

140,608

141,833

Explanation:

a4 = a2 * a2  and  b6= b2 * b* b2

Therefore a4 + b6 = 35 * 35 + 52 * 52 * 52 = 1,225 + 140,608 = 141,833

### Example Question #29 : How To Add Exponents

If , what is the value of ?

Explanation:

Since we have two ’s in  we will need to combine the two terms.

For  this can be rewritten as

So we have .

Or

Divide this by

Thus  or

*Hint: If you are really unsure, you could have plugged in the numbers and found that the first choice worked in the equation.

Solve for x.

2+ 2x+1 = 72

4

7

6

5

3

5

Explanation:

8 + 2x+1 = 72

2x+1 = 64

2x+1 = 26

x + 1 = 6

x = 5

### Example Question #3 : 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?

5

0

5b–1

1/5

1

0

Explanation:

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

### Example Question #4 : How To Add Exponents

If, then what does  equal?

Explanation:

### Example Question #5 : How To Add Exponents

Simplify.  All exponents must be positive.

Explanation:

Step 1:

Step 2:

### Example Question #6 : How To Add Exponents

Simplify.  All exponents must be positive.

Explanation:

Step 1:

Step 2:

Step 3:

### Example Question #7 : How To Add Exponents

Answer must be with positive exponents only.

Explanation:

Step 1:

Step 2: The above is equal to

Evaluate:

Explanation:

Simplify: