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PSAT Math : Exponents

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Example Questions

Example Question #1 : How To Add Exponents

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

Possible Answers:

141,833

150,000

522

3929

140,608

Correct answer:

141,833

Explanation:

a⁴= a² * a² and b⁶= b² * b²* b²

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

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Example Question #94 : Exponents

If $9^{(x + 5)}+3^{2(x+5)}=162$ , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Since we have two ’s in $9^{(x + 5)} + 3^{2(x + 5)}$ we will need to combine the two terms.

For $3^{2(x + 5) }$ this can be rewritten as

$(3^2)^{ (x + 5)} = 9^ {(x + 5)}$

So we have $9^{ (x + 5) }+ 9^{ (x + 5)} = 162$ .

Or $2 (9^{ (x + 5)}) = 162$

Divide this by : $9^{ (x + 5)} = 81 = 9^ 2$

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.

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Example Question #2 : How To Add Exponents

Solve for x.

2³+ 2^x+1= 72

Possible Answers:

Correct answer:

Explanation:

The answer is 5.

8 + 2^x+1= 72

2^x+1= 64

2^x+1= 2⁶

x + 1 = 6

x = 5

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Example Question #3 : How To Add Exponents

Which of the following is eqivalent to 5^b – 5^(b–1) – 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1), where b is a constant?

Possible Answers:

5^b–1

1/5

Correct answer:

Explanation:

We want to simplify 5^b – 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:

5^b – 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1)= 5^b +(–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:

5^b +(–5^(b–1))5 = 5^b + (–1)(5^(b–1))(5) = 5^b – (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, a^ba^c = a^b+c. We can rewrite 5 as 5¹ and then apply this rule.

5^b – (5^(b–1))(5) = 5^b – (5^(b–1))(5¹) = 5^b – 5^(b–1+1)

Now, we will simplify the exponent b – 1 + 1 and write it as simply b.

5^b – 5^(b–1+1)= 5^b – 5^b = 0

The answer is 0.

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Example Question #4 : How To Add Exponents

If $x^2=11$ , then what does $x^4$ equal?

Possible Answers:

121

110

144

Correct answer:

121

Explanation:

$x^4=(x^2)(x^2)=11\cdot 11=121$

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Example Question #5 : How To Add Exponents

Simplify. All exponents must be positive.

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

Possible Answers:

$x^{3}y^{-2}$

$x^{2}y^{7}$

$x^{7}y^{7}$

$\frac{x^{3}}{y}$

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

Correct answer:

$\frac{x^{3}}{y}$

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): $\frac{x^{3}}{y}$

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Example Question #6 : How To Add Exponents

Simplify. All exponents must be positive.

$\frac{x^{-3}y^{5}}{x^{2}y^{-1}}$

Possible Answers:

$x^{-1}y^{4}$

$x^{-5}y^{6}$

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

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

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

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

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Example Question #7 : How To Add Exponents

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

Answer must be with positive exponents only.

Possible Answers:

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

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

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

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

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

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

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Example Question #8 : How To Add Exponents

Evaluate:

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

Possible Answers:

Correct answer:

Explanation:

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

$(-3^{0})=-1$

-1-(-1)=-1+1=0

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Example Question #9 : How To Add Exponents

Simplify:

$3\sqrt{18} + 2\sqrt{50}$

Possible Answers:

$10\sqrt{2}$

$9\sqrt{2}$

$19\sqrt{2}$

$5\sqrt{68}$

$None\ of\ the\ above$

Correct answer:

$19\sqrt{2}$

Explanation:

$3\sqrt{18} = 3\sqrt{2\star 3^{2}} = 9\sqrt{2}$

Similarly $2\sqrt{50} = 2\sqrt{2\star 5^{2}} = 10\sqrt{2}$

So $9\sqrt{2} + 10\sqrt{2}= 19\sqrt{2}$

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PSAT Math : Exponents

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Add Exponents

Example Question #94 : Exponents

Example Question #2 : How To Add Exponents

Example Question #3 : How To Add Exponents

Example Question #4 : How To Add Exponents

Example Question #5 : How To Add Exponents

Example Question #6 : How To Add Exponents

Example Question #7 : How To Add Exponents

Example Question #8 : How To Add Exponents

Example Question #9 : How To Add Exponents

All PSAT Math Resources

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