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GED Math : Exponents

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Example Question #11 : Exponents

Order from least to greatest:

$7^{-2}, 5 ^{-2}, 2 ^{-6}$

Do not use a calculator.

Possible Answers:

$2 ^{-6}, 7^{-2}, 5 ^{-2}$

$5 ^{-2} , 2 ^{-6}, 7^{-2}$

$7^{-2}, 2 ^{-6},5 ^{-2}$

$2 ^{-6}, 5 ^{-2} , 7^{-2}$

Correct answer:

$2 ^{-6}, 7^{-2}, 5 ^{-2}$

Explanation:

For any nonzero and for any , $a^{-m} = \frac{1}{a^{m}}$ .

$7^{-2} = \frac{1}{7^{2}} = \frac{1}{7 \times 7 } = \frac{1}{49}$

$5 ^{-2} = \frac{1}{5 ^{2}} = \frac{1}{5 \times 5} = \frac{1}{25}$

$2 ^{-6} = \frac{1}{2 ^{6}} = \frac{1}{2 \times 2 \times 2 \times 2 \times 2 \times 2 } = \frac{1}{64}$

Since 25 <49 < 64 ,

we can reverse the order when taking their reciprocals:

$\frac{1}{64} < \frac{1}{49}<\frac{1}{25}$

That is, $2 ^{-6}< 7^{-2}< 5 ^{-2}$ .

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Example Question #12 : Exponents

Order from least to greatest:

$\left (-5 \right )^{-3}, \left (-4 \right )^{-3}, \left ( -2\right ) ^{-7}$

Do not use a calculator.

Possible Answers:

$\left (-5 \right )^{-3} , \left (-4 \right )^{-3} , \left ( -2\right ) ^{-7}$

$\left ( -2\right ) ^{-7}, \left (-4 \right )^{-3} , \left (-5 \right )^{-3}$

$\left (-4 \right )^{-3} , \left (-5 \right )^{-3} , \left ( -2\right ) ^{-7}$

$\left ( -2\right ) ^{-7} , \left (-5 \right )^{-3}, \left (-4 \right )^{-3}$

Correct answer:

$\left (-4 \right )^{-3} , \left (-5 \right )^{-3} , \left ( -2\right ) ^{-7}$

Explanation:

For any nonzero and for any , $a^{-m} = \frac{1}{a^{m}}$ .

Also, any negative number raised to the power of an odd number is equal to the opposite of the same power of its absolute value.

Combine these concepts:

$\left (-5 \right )^{-3} = \frac{1 }{\left (-5 \right )^{3}} = \frac{1}{- (5^{3})} = -\frac{1}{125}$

$\left (-4 \right )^{-3} = \frac{1 }{\left (-4 \right )^{3}} = \frac{1}{- (4^{3})} = -\frac{1}{64}$

$\left ( -2\right ) ^{-7} = \frac{1}{\left ( -2\right )^{7}} = \frac{1}{- \left ( 2 ^{7}\right )} = - \frac{1}{128}$

Since 64< 125 < 128 ,

the reciprocals are in reverse order of this:

$\frac{1}{64}> \frac{1}{125 }>\frac{1}{128}$

Their opposites reverse again:

$-\frac{1}{64}<- \frac{1}{125 }<-\frac{1}{128}$

Or, equivalently,

$\left (-4 \right )^{-3} < \left (-5 \right )^{-3} < \left ( -2\right ) ^{-7}$ .

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Example Question #13 : Exponents

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

Possible Answers:

$\frac{1}{2}$

$\frac{1}{16}$

$\frac{1}{32}$

$\frac{1}{12}$

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 #11 : Exponents

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

Possible Answers:

$\frac{2}{3}$

$\frac{2}{9}$

$\frac{1}{3}$

$\frac{1}{27}$

$\frac{2}{27}$

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^4

m^3

m^2

m^1

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 #153 : Complex Operations

Multiply the following:

$h^7 \cdot h^2$

Possible Answers:

h^3

h^9

h^5

h^7

$h^{14}$

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 #17 : Exponents

Divide the following:

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

Possible Answers:

$a^{16}$

a^3

a^8

a^4

a^2

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 #18 : Exponents

Multiply the following:

$x^9 \cdot x^2$

Possible Answers:

x^4

$x^{12}$

$x^{18}$

$x^{11}$

x^3

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 #19 : Exponents

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 #481 : Numbers And Operations

Divide the following:

$n^8 \div n^2$

Possible Answers:

n^4

n^3

n^6

$n^{10}$

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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GED Math : Exponents

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #11 : Exponents

Example Question #12 : Exponents

Example Question #13 : Exponents

Example Question #11 : Exponents

Example Question #482 : Numbers And Operations

Example Question #153 : Complex Operations

Example Question #17 : Exponents

Example Question #18 : Exponents

Example Question #19 : Exponents

Example Question #481 : Numbers And Operations

All GED Math Resources

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