PSAT Math : How to add exponents

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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Example Question #1 : How To Add Exponents

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

Possible Answers:

141,833

140,608

3929

522

150,000

Correct answer:

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 #2253 : Sat Mathematics

If 9(x + 5) + 32(x + 5) = 162, what is the value of x?

Possible Answers:

-3

0

-1

3

1

Correct answer:

-3

Explanation:

Since we have two x’s in 9(x + 5) + 32(x + 5) we will need to combine the two terms.

For 32(x + 5) this can be rewritten as

(32) (x + 5) = 9 (x + 5) 

So we have 9 (x + 5) + 9 (x + 5) = 162.

Or 2 (9 (x + 5)) = 162

Divide this by 2: 9 (x + 5) = 81 = 9 2

Thus x +5 = 2 or x = -3

*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 #2 : Exponents

Solve for x. 

2+ 2x+1 = 72

Possible Answers:

6

3

7

5

4

Correct answer:

5

Explanation:

The answer is 5. 

8 + 2x+1 = 72

      2x+1 = 64

      2x+1 = 26

      x + 1 = 6

           x = 5

Example Question #3 : 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?

Possible Answers:

5

1

1/5

0

5b–1

Correct answer:

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

The answer is 0.

Example Question #2 : How To Add Exponents

Ifx^2=11, then what does x^4 equal?

Possible Answers:

Correct answer:

Explanation:

Example Question #5 : Exponents

Simplify.  All exponents must be positive.

\left ( x^{-2}y^{3} \right )\left ( x^{5}y^{-4} \right )

Possible Answers:

\left ( x^{-2}+x^{5} \right )\left ( y^{3}+y^{-4} \right )

x^{3}y^{-1}

Correct answer:

Explanation:

Step 1: \left ( x^{-2}x^{5} \right )= x^{3}

Step 2: \left ( y^{3}y^{-4} \right )= y^{-1}= \frac{1}{y}

Step 3: (Correct Answer): \frac{x^{3}}{y}

Example Question #6 : Exponents

Simplify.  All exponents must be positive.

Possible Answers:

\frac{1}{x^{5}y^{-6}}

x^{-5}y^{6}

\frac{\left ( xy \right )^{2}}{\left ( xy \right )}

x^{-1}y^{4}

\frac{y^{6}}{x^{5}}

Correct answer:

\frac{y^{6}}{x^{5}}

Explanation:

Step 1: \frac{y^{5}}{\left ( x^{3}x^{2} \right )\left \right )y^{-1}}

 

Step 2: \frac{\left ( y^{5}y^{1} \right )}{x^{3}x^{2}}

Step 3:\frac{y^{6}}{x^{5}}

Example Question #3 : How To Add Exponents

\frac{\left ( -11 \right )^{-8}}{\left ( -11\right )^{12}}

Answer must be with positive exponents only.

Possible Answers:

\left ( -11 \right )^{-20}

\left ( -11 \right )^{4}

\frac{1}{\left ( -11 \right )^{20}}

\left ( 1 \right )^{-20}

\frac{1}{\left ( -11 \right )^{4}}

Correct answer:

\frac{1}{\left ( -11 \right )^{20}}

Explanation:

Step 1:\frac{1}{\left ( -11 \right )^{12}\left ( -11 \right )^{8}}

Step 2: The above is equal to \frac{1}{\left ( -11 \right )^{20}}

Example Question #4 : How To Add Exponents

Evaluate:

 -\left ( -3 \right )^{0}-\left ( -3^{0} \right )

Possible Answers:

Correct answer:

Explanation:

-\left ( -3 \right )^{0}= -1

 

Example Question #9 : How To Add Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

Similarly

 

So

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