PSAT Math : Exponents

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #11 : Exponents

Solve for :

 

Possible Answers:

Correct answer:

Explanation:

If

Then

and

Hence

Example Question #12 : How To Multiply Exponents

Possible Answers:

Correct answer:

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+2 y6+1 z1+3

x5y7z4

Example Question #495 : Algebra

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

Possible Answers:

Correct answer:

Explanation:

To find the answer we can apply the equation of population  where  is the number of hours. 

Example Question #11 : Exponents

Simplify:  2a^{2}b(ab^{2} - a^{2}b)

Possible Answers:

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

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

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

ab^{2} - a^{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}

Example Question #12 : Exponents

Simplify:

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

Possible Answers:

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

Correct answer:

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.

Example Question #11 : Exponents

If , then what is the value of ?

Possible Answers:

Correct answer:

Explanation:

c4 is equal to (c2)(c2).

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

Example Question #11 : Exponents

If  and  are nonzero numbers such that , which of the following is equivalent to ?

Possible Answers:


Correct answer:

Explanation:

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

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.

Example Question #21 : Exponents

If  and  are positive integers and , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

The question tells us that 22a ( 22b )= 16.

We can rewrite 16 as 24, giving us 22a ( 22b )= 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

Example Question #501 : Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

Apply the the various properties of exponents:

 

Example Question #51 : Exponents

Possible Answers:

Correct answer:

Explanation:

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