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PSAT Math : Exponential Operations

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Example Questions

Example Question #13 : Exponents

Solve for :

$\left ( x \right )^{\frac{3}{5}} = 8$

Possible Answers:

$\frac{1}{8}$

$\frac{1}{32}$

Correct answer:

Explanation:

$\left ( x \right )^{\frac{3}{5}} = 8$

Then

$\left \left ((x \right ) ^{\frac{3}{5}} \right )^{\frac{5}{3}} = 8^{\frac{5}{3}}$

$8^{\frac{5}{3}} = 32$ and $\left ( \left ( x \right ) ^{\frac{3}{5}}\right )^{\frac{5}{3}} = x$

Hence x=32

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Example Question #11 : Exponents

(x^3y^6z)(x^2yz^3)=

Possible Answers:

x^6y^6z^3

x^5y^7z^4

x^3y^6z^3

x^5y^7z^3

x^2y^7z^3

Correct answer:

x^5y^7z^4

Explanation:

(x³y⁶z)(x²yz³)

The paraentheses are irrelevant. Rearrange to combine like terms.

x³x²y⁶y¹z¹z³

When you multiply variables with exponents, simply add the exponents together.

x³⁺²y⁶⁺¹z¹⁺³

x⁵y⁷z⁴

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Example Question #51 : Exponential Operations

If an original bacteria colony contains six organisms, and triples every hour, how many organisms are there after 7 hours?

Possible Answers:

4374

107,008

39,366

13,122

Correct answer:

13,122

Explanation:

To find the answer we can apply the equation of population $P=6\cdot 3^{n}$ where is the number of hours.

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Example Question #52 : Exponential Operations

Simplify: $2a^{2}b(ab^{2} - a^{2}b)$

Possible Answers:

$2a^{3}b^{3} + a^{2}b^{2}$

$2a^{3}b^{3} - 2a^{4}b^{2}$

$ab^{2} - a^{2}b$

$2ab^{2} - 2a^{2}b$

$2a^{2}b + 2a^{4}b^{2}$

Correct answer:

$2a^{3}b^{3} - 2a^{4}b^{2}$

Explanation:

Use the distributive property: $a(b+c)=ab+ac$ . When we multiply variables with exponents, we keep the same base and add the exponents: $a^{m}a^{n} = a^{m+n}$

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Example Question #12 : Exponential Operations

Simplify:

$(6x^{2})^{2}\times y^{2} + xyz =$

Possible Answers:

$\textbf{cannot be simplified}$

$36x^{5}y^{3}z$

$36x^{4}y^{2}$

$6x^{4}y^{2}z + xyz$

$36x^{4}y^{2}+xyz$

Correct answer:

$36x^{4}y^{2}+xyz$

Explanation:

$(6x^{2})^{2} = 6^{2}x^{4} = 36x^{4}$

$36x^{4}\times y^{2} = 36x^{4}y^{2}$

We cannot combine $36x^{4}y^{2}$ with $xyz$ , so $(6x^{2})^{2}\times y^{2} + xyz =36x^{4}y^{2}+xyz$ .

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Example Question #12 : Exponents

If c^2=15 , then what is the value of c^4 ?

Possible Answers:

125

225

110

$\sqrt{15}$

Correct answer:

225

Explanation:

c⁴ is equal to (c²)(c²).

We know c² = 15. Plugging in this value gives us c⁴ = (15)(15) = 225.

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Example Question #19 : Exponents

If and are nonzero numbers such that a^2 = b^3 , which of the following is equivalent to a^6 ?

Possible Answers:

b^9

b^8

b^7

$b^{11}$

b^6

Correct answer:

b^9

Explanation:

For this problem, we need to make use of the property of exponents, which states that (x^y)^z = x^y^z.

We are given a² but are asked to find a⁶.

Let's raise both sides of the equation to the third power, so that we will end up with a⁶ on the left side.

(a²)³ = (b³)³

Now, according to the property of exponents mentioned before, we can multiply the exponents.

a^(2*3) = b^(3*3)

a⁶ = b⁹

The answer is b⁹.

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Example Question #53 : Exponential Operations

If and are positive integers and $2^{2a}(2^{2b})=16$ , what is the value of a +b ?

Possible Answers:

Correct answer:

Explanation:

The question tells us that 2^2a ( 2^2b)= 16.

We can rewrite 16 as 2⁴, giving us 2^2a ( 2^2b)= 2⁴.

When terms with the same base are multipled, their exponents can be added:

2^{(2a +2b)}= 2⁴

Since the base is the same on both sides of the equation, we can equate the exponents:

2a +2b = 4

2(a + b) = 4

a + b = 2

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Example Question #51 : Exponents

Simplify:

$\left ( \frac{x}{2t^{2}} \right )^{3}$

Possible Answers:

$\frac{x^{3}}{ 9t^{6} }$

$\frac{x^{3}}{ 8 t^{6} }$

$\frac{ 6 t^{6} }{x^{3}}$

$\frac{x^{3}}{ 6 t^{6} }$

$\frac{ 8 t^{6} }{x^{3}}$

Correct answer:

$\frac{x^{3}}{ 8 t^{6} }$

Explanation:

Apply the the various properties of exponents:

$\left ( \frac{x}{2t^{2}} \right )^{3}$

$=\frac{x^{3}}{ \left ( 2t^{2} \right ) ^{3}}$

$=\frac{x^{3}}{ 2^{3} \left ( t^{2} \right )^{3} }$

$=\frac{x^{3}}{ 8 t^{2 \cdot 3} }$

$=\frac{x^{3}}{ 8 t^{6} }$

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Example Question #22 : How To Multiply Exponents

$\textup{If }4^{3}\times8^{2}=2^{y}\textup{, what is the value of }y\textup{ ?}$

Possible Answers:

Correct answer:

Explanation:

$\textup{4 and 8 are powers of 2. Find the common base and set exponents equal:}$

$\left ( 2^{2}\right )^{3}\times \left ( 2^{3}\right )^{2}=2^{y}\: \; \; \; \; \; \;2^{6}\times 2^{6}=2^{y}$

$2^{12}=2^{y}\: \: \: \: \: \: \:12=y$

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PSAT Math : Exponential Operations

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #13 : Exponents

Example Question #11 : Exponents

Example Question #51 : Exponential Operations

Example Question #52 : Exponential Operations

Example Question #12 : Exponential Operations

Example Question #12 : Exponents

Example Question #19 : Exponents

Example Question #53 : Exponential Operations

Example Question #51 : Exponents

Example Question #22 : How To Multiply Exponents

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