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SAT Math : Exponential Operations

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Example Questions

Example Question #481 : Algebra

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

Possible Answers:

6^6

6^4

$6^{8}$

6^8

6^7

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

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Example Question #11 : Exponents

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

I. yx<0

II. yz<0

III. xz<0

Possible Answers:

III

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.

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Example Question #12 : Exponents

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

Possible Answers:

$\frac{1}{9}$

$\frac{1}{3}$

$\frac{2}{6}$

$-\frac{1}{9}$

$-\frac{1}{3}$

Correct answer:

$-\frac{1}{9}$

Explanation:

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

$= \frac{1}{9}$

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

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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 #12 : Exponents

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

Possible Answers:

13,122

107,008

4374

39,366

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 #11 : Exponential Operations

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

Possible Answers:

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

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

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

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

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

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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SAT Math : Exponential Operations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #481 : Algebra

Example Question #11 : Exponents

Example Question #12 : Exponents

Example Question #13 : Exponents

Example Question #11 : Exponents

Example Question #12 : Exponents

Example Question #11 : Exponential Operations

Example Question #12 : Exponential Operations

Example Question #12 : Exponents

Example Question #19 : Exponents

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