PSAT Math : How to multiply exponents

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #11 : Exponents

(x3)2 * x2

Possible Answers:

x2

x4

x6

x

x4

Correct answer:

x4

Explanation:

When an exponent is raised to a power, we multiply. But when two exponents with the same base are multiplied, we add them. So (x3)2 = x3*2 = x6. Then (x3)2 * x2 = x6 * x2 = x6 – 2 = x4.

Example Question #11 : Exponents

If  \sqrt{x}=y^{2}=6, then which of the following is equivalent to x^3y^4?

Possible Answers:

6^7

6^4

6^8

6^{8}

6^6

Correct answer:

6^{8}

Explanation:

We can break up the equation into two smaller equations involving only x and y. Then, once we solve for x and y, we can find the value of x^3y^4.

Simp_sqrt1

Example Question #41 : Exponents

If y^7x^8z^2 <0 which of the following must be true?

I. 

II. 

III. 

Possible Answers:

I

III

None

All

II

Correct answer:

None

Explanation:

 must be negative because it has an odd power and  and  have even powers above. But  and  could be positive or negative, so none of the scenarios has to be true.

Example Question #11 : How To Multiply Exponents

-\left ( \frac{-1}{3} \right )^{2}

Possible Answers:

\frac{2}{6}

-\frac{1}{9}

\frac{1}{9}

-\frac{1}{3}

\frac{1}{3}

Correct answer:

-\frac{1}{9}

Explanation:

= \frac{\left ( -1 \right )^{2}}{\left ( 3 \right )^{2}}

= \frac{1}{9}

Hence the correct answer will be - \frac{1}{9}

Example Question #11 : Exponents

Solve for :

 

Possible Answers:

Correct answer:

Explanation:

If

Then

and

Hence

Example Question #51 : 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 #51 : Exponents

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 #491 : Algebra

Simplify:  2a^{2}b(ab^{2} - a^{2}b)

Possible Answers:

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

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

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

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

2a^{3}b^{3} + a^{2}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 #492 : Algebra

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.

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