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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #145 : Multiplying And Dividing Exponents

Simplify: $\frac{2^{12}}{4^6}$

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

$\frac{1}{2}$

Correct answer:

Explanation:

Although the exponents have different bases, we know that 4=2^2 . Therefore we can rewrite as $\frac{2^{12}}{4^6}=\frac{2^{12}}{(2^2)^6}=\frac{2^{12}}{2^{12}}=1$

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Example Question #149 : Multiplying And Dividing Exponents

Simplify: $\frac{2^{24}8^8}{4^{16}}$

Possible Answers:

2^8

$2^{12}$

$\frac{1}{2^8}$

$2^{16}$

$\frac{1}{2^{12}}$

Correct answer:

$2^{16}$

Explanation:

Although the bases are not the same, we know that 8=2^3, 4=2^2 . We will base our answers in base of since this is present in all the choices. Therefore: $\frac{2^{24}8^8}{4^{16}}=\frac{2^{24}(2^3)^8}{(2^2)^{16}}=\frac{2^{24}2^{24}}{2^{32}}$ Now we add the exponents and then subtract them.

$\frac{2^{24}2^{24}}{2^{32}}=\frac{2^{48}}{2^{32}}=2^{16}$

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Example Question #150 : Multiplying And Dividing Exponents

Divide: $\frac{1}{5}\div 25^{-10}$

Possible Answers:

$\frac{5}{25^{15}}$

$5^{21}$

$25^{15}$

$\frac{5}{25^{21}}$

$5^{19}$

Correct answer:

$5^{19}$

Explanation:

In order to divide, we will first need to change the bases of both terms.

Both terms can be rewritten as base five.

$\frac{1}{5}\div 25^{-10} = 5^{-1} \div 5^{2(-10)} = \frac{5^{-1}}{5^{-20}}$

Now that bases are common, we can subtract the powers and the base will be left unchanged.

$5^{-1-(-20)} = 5^{19}$

The answer is: $5^{19}$

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Example Question #951 : Mathematical Relationships And Basic Graphs

Evaluate: x^5*2x^2

Possible Answers:

2x^7

4x^8

4x^7

$4x^{10}$

$2x^{10}$

Correct answer:

2x^7

Explanation:

When multiplying exponents, we just add the exponents and keep the base the same.

$x^5*2x^2=2x^{5+2}=2x^7$

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Example Question #952 : Mathematical Relationships And Basic Graphs

Evaluate: $3x^7*4x^{-2}$

Possible Answers:

$3^74^{-2}x^9$

12x^5

12x^9

$12x^{-14}$

$3^74^{-2}x^5$

Correct answer:

12x^5

Explanation:

When multiplying exponents, we just add the exponents and keep the base the same.

$3x^7*4x^{-2}=12x^{7+(-2)}=12x^5$

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Example Question #953 : Mathematical Relationships And Basic Graphs

Simplify: $\frac{8^{2x}}{8^{2x-1}}$

Possible Answers:

$\frac{1}{8^{2x}}$

$8^{2x}$

Correct answer:

Explanation:

When dividing exponents, we just subtract the exponents and keep the base the same.

$\frac{8^{2x}}{8^{2x-1}}=8^{2x-(2x-1)}=8^{2x-2x+1}=8^{1}=8$

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Example Question #954 : Mathematical Relationships And Basic Graphs

Simplify: $\frac{x^5y^7}{x^{5+b}y^{7-c}}$

Possible Answers:

-x^by^c

$xy^{b-c}$

$\frac{x^b}{y^c}$

$\frac{y^c}{x^b}$

x^by^c

Correct answer:

$\frac{y^c}{x^b}$

Explanation:

When dividing exponents, we just subtract the exponents and keep the base the same.

$\frac{x^5y^7}{x^{5+b}y^{7-c}}=x^{5-(5+b)y^{7-(7-c)}}=x^{-b}y^c=\frac{y^c}{x^b}$

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Example Question #155 : Multiplying And Dividing Exponents

Solve the exponents: $4(2^{30})(8^{50})$

Possible Answers:

$4^{182}$

$64^{80}$

$32^{80}$

$8^{182}$

$2^{182}$

Correct answer:

$2^{182}$

Explanation:

To simplify, we will need to convert all bases to a common base to apply exponent properties.

2=2^1, 4=2^2, 8=2^3

We can rewrite each term using the powers of two.

$4(2^{30})(8^{50}) = (2^2)(2^{30})(2^{3(50)})= (2^2)(2^{30})(2^{150})$

Simplify the exponents. Since powers of same bases are multiplied, the powers can be added.

$2^{2+30+150} = 2^{182}$

The answer is: $2^{182}$

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Example Question #156 : Multiplying And Dividing Exponents

Divide: $\frac{6^{-2}}{3^{-3}}$

Possible Answers:

$\frac{4}{3}$

$\frac{1}{32}$

$\frac{3}{4}$

Correct answer:

$\frac{3}{4}$

Explanation:

Simplify the negative exponents by rewriting the terms as fractions.

$\frac{6^{-2}}{3^{-3}} = \frac{\frac{1}{6^2}}{\frac{1}{3^3}}= \frac{\frac{1}{36}}{\frac{1}{27}}$

Divide the complex fractions.

$\frac{1}{36} \div \frac{1}{27} = \frac{1}{36} \times 27 =\frac{27}{36}$

Reduce this fraction.

The answer is: $\frac{3}{4}$

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Example Question #157 : Multiplying And Dividing Exponents

Divide the exponents: $\frac{8^6}{4^8}$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{2}$

Correct answer:

Explanation:

Change the base of the numerator and denominator.

They both can be rewritten as a base of two.

$\frac{8^6}{4^8} = \frac{2^{3(6)}}{2^{2(8)}} = \frac{2^{18}}{2^{16}}$

Since the bases are similar, we can subtract the exponents.

$2^{18-16} = 2^2 =4$

The answer is:

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #145 : Multiplying And Dividing Exponents

Example Question #149 : Multiplying And Dividing Exponents

Example Question #150 : Multiplying And Dividing Exponents

Example Question #951 : Mathematical Relationships And Basic Graphs

Example Question #952 : Mathematical Relationships And Basic Graphs

Example Question #953 : Mathematical Relationships And Basic Graphs

Example Question #954 : Mathematical Relationships And Basic Graphs

Example Question #155 : Multiplying And Dividing Exponents

Example Question #156 : Multiplying And Dividing Exponents

Example Question #157 : Multiplying And Dividing Exponents

All Algebra II Resources

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