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GED Math : Exponents

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Example Question #31 : Exponents

Simplify the following:

$h^3 \cdot h^9$

Possible Answers:

h^6

h^9

h^3

$h^{12}$

$h^{27}$

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 #500 : 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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Example Question #31 : Exponents

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

Possible Answers:

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

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

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

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

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 #32 : Exponents

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

Possible Answers:

$\frac{9}{4}$

$\frac{2}{9}$

$\frac{4}{3}$

$\frac{1}{9}$

$\frac{1}{36}$

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 #31 : Exponents

Combine the following:

$x^3 \cdot x^5$

Possible Answers:

$x^{35}$

x^8

x^7

x^2

$x^{15}$

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 #32 : Exponents

Simplify the following:

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

Possible Answers:

m^8

m^5

m^6

m^7

$m^{12}$

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 #31 : Exponents

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 #36 : 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 #37 : Exponents

Simplify the following:

$s^7 \cdot s^2$

Possible Answers:

s^9

$2s^{14}$

s^5

$s^{14}$

2s^9

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 #31 : Exponents

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

Possible Answers:

$\frac{1}{243}$

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

$\frac{1}{18}$

$\frac{1}{15}$

$\frac{1}{729}$

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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GED Math : Exponents

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #31 : Exponents

Example Question #500 : Numbers And Operations

Example Question #31 : Exponents

Example Question #32 : Exponents

Example Question #31 : Exponents

Example Question #32 : Exponents

Example Question #31 : Exponents

Example Question #36 : Exponents

Example Question #37 : Exponents

Example Question #31 : Exponents

All GED Math Resources

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