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GED Math : Complex Operations

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Example Questions

Example Question #151 : Complex Operations

Solve: $2^2\div 4^{3}$

Possible Answers:

$\frac{1}{2}$

$\frac{1}{16}$

$\frac{1}{12}$

$\frac{1}{32}$

Correct answer:

$\frac{1}{16}$

Explanation:

Evaluate each term first.

2^2 =4

4^3 = 64

Divide 4 with 64 and reduce.

$\frac{4}{64} = \frac{(4\times 1)}{(4\times 16)}$

The answer is: $\frac{1}{16}$

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Example Question #481 : Numbers And Operations

Simplify: $\frac{2^3}{6^2}$

Possible Answers:

$\frac{2}{3}$

$\frac{2}{9}$

$\frac{1}{3}$

$\frac{2}{27}$

$\frac{1}{27}$

Correct answer:

$\frac{2}{9}$

Explanation:

Do not subtract the exponents or divide the bases! We will need to compute the numerator and denominator first.

$\frac{2^3}{6^2} = \frac{(2)(2)(2)}{(6)(6)} = \frac{8}{36}$

Reduce this fraction.

The answer is: $\frac{2}{9}$

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Example Question #482 : Numbers And Operations

Divide the following:

$m^6 \div m^2$

Possible Answers:

m^1

m^4

m^3

m^2

m^3

Correct answer:

m^4

Explanation:

To divide variables with exponents, we will use the following formula:

$x^a \div x^b = x^{a-b}$

So, we get

$m^6 \div m^2 = m^{6-2}$

$m^6 \div m^2 = m^4$

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Example Question #483 : Numbers And Operations

Multiply the following:

$h^7 \cdot h^2$

Possible Answers:

$h^{14}$

h^3

h^5

h^9

h^7

Correct answer:

h^9

Explanation:

To multiply variables with exponents, we will use the following formula:

$x^a \cdot x^b = x^{a+b}$

So we get

$h^7 \cdot h^2 = h^{7+2}$

$h^7 \cdot h^2 = h^9$

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Example Question #12 : Exponents

Divide the following:

$a^{12} \div a^4$

Possible Answers:

a^8

$a^{16}$

a^4

a^2

a^3

Correct answer:

a^8

Explanation:

To divide variables with exponents, we will use the following formula:

$x^a \div x^b = x^{a-b}$

Now, let’s divide. We get

$a^{12} \div a^4 = a^{12-4}$

$a^{12} \div a^4 = a^8$

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Example Question #14 : Exponents

Multiply the following:

$x^9 \cdot x^2$

Possible Answers:

x^4

$x^{12}$

x^3

$x^{18}$

$x^{11}$

Correct answer:

$x^{11}$

Explanation:

To multiply variables with exponents, we will use the following formula:

$x^a \cdot x^b = x^{a+b}$

Now, we will multiply. We get

$x^9 \cdot x^2 = x^{9 + 2}$

$x^9 \cdot x^2 = x^{11}$

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Example Question #484 : Numbers And Operations

Divide: $\frac{(-2)^3}{(-4)^{-1}}$

Possible Answers:

$\frac{1}{2}$

Correct answer:

Explanation:

Simplify the numerator.

(-2)^3=(-2)(-2)(-2) = -8

Simplify the denominator.

$(-4)^{-1} = \frac{1}{(-4)^1} =-\frac{1}{4}$

Divide the terms.

$\frac{(-2)^3}{(-4)^{-1}} = \frac{-8}{-\frac{1}{4}} = -8\div- \frac{1}{4}$

Take the reciprocal of the second term and change the sign to a multiplication.

$-8\div- \frac{1}{4} = -8\times -4 = 32$

The answer is:

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Example Question #158 : Complex Operations

Divide the following:

$n^8 \div n^2$

Possible Answers:

$n^{10}$

n^4

n^3

n^6

n^2

Correct answer:

n^6

Explanation:

To divide variables with exponents, we will use the following formula:

$x^a \div x^b = x^{a-b}$

So, we get

$n^8 \div n^2 = n^{8-2}$

$n^8 \div n^2 = n^6$

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Example Question #159 : Complex Operations

Multiply the following:

$k^3 \cdot k^3$

Possible Answers:

k^9

k^3

k^2

k^1

k^6

Correct answer:

k^6

Explanation:

To multiply variables with exponents, we will use the following formula:

$x^a \cdot x^b = x^{a+b}$

So we get

$k^3 \cdot k^3 = k^{3+3}$

$k^3 \cdot k^3 = k^6$

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Example Question #485 : Numbers And Operations

Divide the following:

$g^{14} \div g^2$

Possible Answers:

g^7

g^2

$g^{16}$

$g^{12}$

g^8

Correct answer:

$g^{12}$

Explanation:

To divide variables with exponents, we will use the following formula:

$x^a \div x^b = x^{a-b}$

Now, let’s divide. We get

$g^{14} \div g^2 = g^{14-2}$

$g^{14} \div g^2 = g^{12}$

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All GED Math Resources

4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

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GED Math : Complex Operations

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #151 : Complex Operations

Example Question #481 : Numbers And Operations

Example Question #482 : Numbers And Operations

Example Question #483 : Numbers And Operations

Example Question #12 : Exponents

Example Question #14 : Exponents

Example Question #484 : Numbers And Operations

Example Question #158 : Complex Operations

Example Question #159 : Complex Operations

Example Question #485 : Numbers And Operations

All GED Math Resources

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