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PSAT Math : How to multiply exponents

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Example Questions

Example Question #7 : Exponents

(x³)² * x^–² =

Possible Answers:

x²

x^–⁴

x⁴

x⁶

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 = x^3*2 = x⁶. Then (x³)² * x^–² = x⁶ * x^–² = x^6 – 2 = x⁴.

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Example Question #41 : Exponents

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

Possible Answers:

$6^{8}$

6^7

6^4

6^6

6^8

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 #42 : 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:

None

All

III

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 #11 : Exponents

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

Possible Answers:

$\frac{1}{9}$

$\frac{1}{3}$

$-\frac{1}{9}$

$\frac{2}{6}$

$-\frac{1}{3}$

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 #12 : Exponents

Solve for :

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

Possible Answers:

$\frac{1}{32}$

$\frac{1}{8}$

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 #51 : Exponents

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

Possible Answers:

x^3y^6z^3

x^5y^7z^3

x^2y^7z^3

x^5y^7z^4

x^6y^6z^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 #52 : Exponents

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

Possible Answers:

4374

13,122

39,366

107,008

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 #53 : Exponents

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

Possible Answers:

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

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

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

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

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

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: $a^{m}a^{n} = a^{m+n}$

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Example Question #11 : How To Multiply Exponents

Simplify:

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

Possible Answers:

$\textbf{cannot be simplified}$

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

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

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

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

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 #11 : Exponents

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

Possible Answers:

$\sqrt{15}$

125

110

225

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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PSAT Math : How to multiply exponents

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #7 : Exponents

Example Question #41 : Exponents

Example Question #42 : Exponents

Example Question #11 : Exponents

Example Question #12 : Exponents

Example Question #51 : Exponents

Example Question #52 : Exponents

Example Question #53 : Exponents

Example Question #11 : How To Multiply Exponents

Example Question #11 : Exponents

All PSAT Math Resources

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