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GED Math : Complex Operations

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Example Questions

Example Question #161 : Complex Operations

Multiply the following:

$q^5 \cdot q^2$

Possible Answers:

q^3

$q^{25}$

$q^{7}$

$q^{10}$

q^4

Correct answer:

$q^{7}$

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

$q^5 \cdot q^2 = q^{5 + 2}$

$q^5 \cdot q^2 = q^{7}$

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Example Question #24 : Exponents

$A = (-7)^{2}$

$B = -7^{2}$

Which is true of and ?

Possible Answers:

A =B = 49

A = 49 and B = -49

A = - 49 and B = 49

A =B = -49

Correct answer:

A = 49 and B = -49

Explanation:

The square of a number is the product of the number and itself.

$A = (-7)^{2} = (-7 ) \times (-7)$

The product of two negative numbers is equal to the (positive) product of their (positive) absolute values, so

$A = (-7 ) \times (-7) = 7 \times 7 = 49$

$B = -7^{2}$ , which means that is equal to the opposite of the square of 7; that is,

$B = - (7^{2}) = -(7 \times 7) = -49$

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Example Question #161 : Complex Operations

Evaluate: $\frac{9^2}{2^3}$

Possible Answers:

$\frac{81}{8}$

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

$\frac{27}{2}$

Correct answer:

$\frac{81}{8}$

Explanation:

Simplify the numerator and denominator.

$\frac{9^2}{2^3} = \frac{9(9)}{2(2)(2)} = \frac{81}{8}$

The answer is: $\frac{81}{8}$

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Example Question #492 : Numbers And Operations

Simplify:

3^4*(3^2)^4

Possible Answers:

3^1^0

3^3^2

3^4^0

3^2^4

3^1^2

Correct answer:

3^1^2

Explanation:

Recall that when you have a power to another power, you multiply their exponents. This means that:

(3^2)^4=3^8

Therefore, you can rewrite your question:

3^4*3^8

Next, recall that when you multiply numbers of the same base, you add the exponents. Thus, you can simplify:

3^4*3^8=3^1^2

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Example Question #164 : Complex Operations

Simplify:

3^2*6^5*2

Possible Answers:

2^1^2*3^1^4

Cannot be simplified

2^7*3^5

2^6*3^7

2^3*3^9

Correct answer:

2^6*3^7

Explanation:

For a question like this, it can help to rewrite the as 2*3 . We are doing this because the answer is given in terms of prime values:

3^2*6^5*2=3^2*(3*2)^5*2

Now, you can "distribute" the power of :

3^2*(3*2)^5*2=3^2*3^5*2^5*2

For numbers of the same base, you just need to add the powers:

3^2*3^5*2^5*2=2^6*3^7

Given the form of the answer options, this suffices!

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Example Question #495 : Numbers And Operations

Simplify:

$\frac{5^1^07^1^2}{25^2*14}$

Possible Answers:

$\frac{5^87^1^1}{2}$

$\frac{5^47^1^0}{2}$

$\frac{5^67^1^1}{2}$

$\frac{5^67^1^2}{14}$

None of the others

Correct answer:

$\frac{5^67^1^1}{2}$

Explanation:

Begin by breaking apart the values in the denominator:

$\frac{5^1^07^1^2}{25^2*14}=\frac{5^1^07^1^2}{(5*5)^2*2*7}$

Now, you can go another step:

$\frac{5^1^07^1^2}{(5^2)^2*2*7}$

Now, simplify the (5^2)^2 by multiplying the exponents:

$\frac{5^1^07^1^2}{(5)^4*2*7}$

Now, just "reorganize things":

$\frac{5^1^07^1^2}{2*5^4*7}$

Finally, you can cancel out the appropriate s and the :

$\frac{5^67^1^1}{2}$

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Example Question #165 : Complex Operations

Simplify the following:

$\frac{x^-^4y^3}{x^8y^5}$

Possible Answers:

$\frac{1}{x^1^2y^-^2}$

$\frac{y^2}{x^1^2}$

$\frac{1}{x^4y^2}$

$\frac{y^3}{x^4y^5}$

$\frac{1}{x^1^2y^2}$

Correct answer:

$\frac{1}{x^1^2y^2}$

Explanation:

Remember that for negative exponent values, you "flip" the number over the bar of the fraction of which it is a part. When you do this, you then make its power positive. You should always start by doing this. It makes it easier for most students to understand the reductions that follow upon that.

Thus, for your value, you know:

$\frac{x^-^4y^3}{x^8y^5}=\frac{y^3}{x^4x^8y^5}$

Combine your like variables first. You do this by adding their exponents:

$\frac{y^3}{x^4x^8y^5}=\frac{y^3}{x^1^2y^5}$

Now, cancel the like terms:

$\frac{1}{x^1^2y^2}$

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Example Question #24 : Exponents

$\frac{x^3y^-^9z^-^3}{x^-^4y^4z^1^0}$

Possible Answers:

$\frac{x^7}{y^1^3z^1^3}$

$\frac{x^4y^5}{z^7}$

$\frac{x}{y^1^3z^1^3}$

$\frac{xy^5}{z^7}$

$\frac{x}{y^-^5z^7}$

Correct answer:

$\frac{x^7}{y^1^3z^1^3}$

Explanation:

Thus, for your value, you know:

$\frac{x^3y^-^9z^-^3}{x^-^4y^4z^1^0}=\frac{x^3x^4}{y^4z^1^0y^9z^3}=\frac{x^3x^4}{y^4y^9z^3z^1^0}$

Combine your like variables first. You do this by adding their exponents:

$\frac{x^3x^4}{y^4y^9z^3z^1^0}=\frac{x^7}{y^1^3z^1^3}$

Luckily, there is no canceling for you to do!

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Example Question #31 : Exponents

Simplify the following:

$h^3 \cdot h^9$

Possible Answers:

$h^{12}$

h^9

$h^{27}$

h^3

h^6

Correct answer:

$h^{12}$

Explanation:

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

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

So, given the problem

$h^3 \cdot h^9$

we can solve. We get

$h^3 \cdot h^9 = h^{3+9}$

$h^3 \cdot h^9 = h^{12}$

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Example Question #497 : Numbers And Operations

Evaluate $(-4)^{5}$ and $-4^{5}$ . Which statement is true of these two values?

Possible Answers:

$(-4)^{5} = -4^{5} = 1,024$

$(-4)^{5} = -1,024$ and $-4^{5} = 1,024$

$(-4)^{5} = -4^{5} = -1,024$

$(-4)^{5} = 1,024$ and $-4^{5} = -1,024$

Correct answer:

$(-4)^{5} = -4^{5} = -1,024$

Explanation:

$(-4)^{5}$ has 5, an odd number, as an exponent, so $(-4)^{5}$ is a negative number, and it can be calculated by taking the opposite of the fifth power of 4.

$-4^{5}$ is equal to the opposite of the fifth power of 4 as well.

Therefore,

$(-4)^{5} = -4^{5} = - (4^{5})$ .

$4^{5} = 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4$

$= 16 \cdot 4 \cdot 4 \cdot 4$

$= 64\cdot 4 \cdot 4$

$=256 \cdot 4$

= 1,024 ,

$(-4)^{5} = -4^{5} = - 1,024$ .

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GED Math : Complex Operations

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #161 : Complex Operations

Example Question #24 : Exponents

Example Question #161 : Complex Operations

Example Question #492 : Numbers And Operations

Example Question #164 : Complex Operations

Example Question #495 : Numbers And Operations

Example Question #165 : Complex Operations

Example Question #24 : Exponents

Example Question #31 : Exponents

Example Question #497 : Numbers And Operations

All GED Math Resources

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