SAT Math : How to multiply exponents

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #11 : Exponents

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

Possible Answers:

6^4

6^{8}

6^8

6^7

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 #12 : Exponents

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

I. 

II. 

III. 

Possible Answers:

III

I

II

None

All

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 : Exponents

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

Possible Answers:

\frac{1}{9}

\frac{2}{6}

-\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 #12 : Exponents

Solve for :

 

Possible Answers:

Correct answer:

Explanation:

If

Then

and

Hence

Example Question #12 : 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 #11 : 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 #12 : Exponents

Simplify:  2a^{2}b(ab^{2} - a^{2}b)

Possible Answers:

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

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

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

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

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

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 #13 : 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 #16 : 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 #17 : 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.

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