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GED Math : Complex Operations

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Example Questions

Example Question #171 : Complex Operations

Evaluate $(-3)^{6}$ and $-3^{6}$ . Which statement is true of these two values?

Possible Answers:

$(-3)^{6} = 729$ and $-3^{6} = -729$

$(-3)^{6} = -3^{6} =- 729$

$(-3)^{6} =- 729$ and $-3^{6} = 729$

$(-3)^{6} = -3^{6} =729$

Correct answer:

$(-3)^{6} = 729$ and $-3^{6} = -729$

Explanation:

$(-3)^{6}$ has 6, an even number, as an exponent, so $(-3)^{6}$ is a positive number, and it can be calculated by taking sixth power of 3.

$-3^{6}$ is the (negative) opposite of the sixth power of 3.

Therefore,

$(-3)^{6} = 3 ^{6} = 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3$

$= 9 \cdot 3 \cdot 3 \cdot 3 \cdot 3$

$= 27 \cdot 3 \cdot 3 \cdot 3$

$= 81 \cdot 3 \cdot 3$

$=243 \cdot 3$

= 729

and

$-3^{6} = - (3^{6})= -729$ .

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Example Question #501 : Numbers And Operations

Evaluate: $(\frac{2}{3}) ^{-2}$

Possible Answers:

$\frac{9}{4}$

$\frac{4}{3}$

$\frac{1}{9}$

$\frac{2}{9}$

$\frac{1}{36}$

Correct answer:

$\frac{9}{4}$

Explanation:

In order to solve, we will need to eliminate the negative exponent. Use the following property of negative exponents.

$x^{-n} = \frac{1}{x^n}$

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

Simplify the denominator.

$\frac{1}{\frac{4}{9}} = 1\div\frac{4}{9}$

Convert the division sign to multiplication and take the reciprocal of the second term.

$1\div\frac{4}{9} = 1\times \frac{9}{4}$

The answer is: $\frac{9}{4}$

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Example Question #501 : Numbers And Operations

Combine the following:

$x^3 \cdot x^5$

Possible Answers:

x^2

x^7

$x^{35}$

x^8

$x^{15}$

Correct answer:

x^8

Explanation:

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

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

Now, let’s combine the following:

$x^3 \cdot x^5 = x^{3+5}$

$x^3 \cdot x^5 = x^8$

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Example Question #502 : Numbers And Operations

Simplify the following:

$\frac{m^{10}}{m^2}$

Possible Answers:

$m^{12}$

m^6

m^7

m^8

m^5

Correct answer:

m^8

Explanation:

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

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

So, we get

$\frac{m^{10}}{m^2} = m^{10-2}$

$\frac{m^{10}}{m^2} = m^8$

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Example Question #172 : Complex Operations

Evaluate: 3-(2^2)^3

Possible Answers:

Correct answer:

Explanation:

Evaluate the second term first.

(2^2)^3 = (2^2)(2^2)(2^2) = (4)(4)(4) = 64

Replace this term.

3-(2^2)^3 = 3-64 = -61

The answer is:

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Example Question #31 : Exponents

Solve: (-1)^3-(2^2)^4

Possible Answers:

Correct answer:

Explanation:

Evaluate each term using order of operations. We can expand the terms in parentheses to eliminate the exponents.

(-1)^3-(2^2)^4 = (-1)(-1)(-1) - (2^2)(2^2)(2^2)(2^2)

Simplify the terms.

=(-1)(-1)(-1) - (2^2)(2^2)(2^2)(2^2)

= (-1)(-1)(-1) -(4)(4)(4)(4)

=-1 -256 = -257

The answer is:

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Example Question #504 : Ged Math

Simplify the following:

$s^7 \cdot s^2$

Possible Answers:

2s^9

$s^{14}$

s^9

$2s^{14}$

s^5

Correct answer:

s^9

Explanation:

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

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

Now, given the problem

$s^7 \cdot s^2$

we can solve. We get

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

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

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Example Question #173 : Complex Operations

Evaluate: $(3^2)^{-3}$

Possible Answers:

$\frac{1}{18}$

$\frac{1}{243}$

$\textup{The answer is not given.}$

$\frac{1}{729}$

$\frac{1}{15}$

Correct answer:

$\frac{1}{729}$

Explanation:

In order to solve, we can simplify by multiplying the powers together according to the rule of exponents.

$(a^{X})^Y = a^{XY}$

$(3^2)^{-3} = 3^{2\times -3} = 3^{-6}$

The negative exponent can be rewritten as a fraction.

$3^{-6} = \frac{1}{3^6} = \frac{1}{729}$

The answer is: $\frac{1}{729}$

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Example Question #174 : Complex Operations

What is the product of (2m^2n^3)^2(-3mn)^2 ?

Possible Answers:

16m^4n^8

36m^6n^8

-36m^2n^4

$36m^4n^{16}$

Correct answer:

36m^6n^8

Explanation:

Start by distributing the exponents into their respective terms. Recall that when an exponent is raised to an exponent, you will need to multiply the exponents together.

(2m^2n^3)^2(-3mn)^2=(4m^4n^6)(9m^2n^2)

Next, multiply like terms together. Recall that when you multiply numbers that have the same base, you will need to add the exponents together.

(4m^4n^6)(9m^2n^2)=36m^6n^8

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Example Question #175 : Complex Operations

What is the product of (5x^2yz^2)^2 and (3y^2)^2 ?

Possible Answers:

275x^4y^6z^2

125x^6y^2z^4

225x^4y^6z^4

225x^4y^4z^4

Correct answer:

225x^4y^6z^4

Explanation:

Since the question asks for the product, we will need to multiply the two terms.

(5x^2yz^2)^2(3y^2)^2

Start by distributing the exponents into the proper terms. Recall that when an exponent is raised to another exponent, you will need to multiply the two exponents together.

(5x^2yz^2)^2(3y^2)^2=(25x^4y^2z^4)(9y^4)

Next, multiply like terms together. Recall that when you multiply numbers that have the same base but different exponents, you will need to add the exponents together.

(25x^4y^2z^4)(9y^4)=225x^4y^6z^4

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GED Math : Complex Operations

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #171 : Complex Operations

Example Question #501 : Numbers And Operations

Example Question #501 : Numbers And Operations

Example Question #502 : Numbers And Operations

Example Question #172 : Complex Operations

Example Question #31 : Exponents

Example Question #504 : Ged Math

Example Question #173 : Complex Operations

Example Question #174 : Complex Operations

Example Question #175 : Complex Operations

All GED Math Resources

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