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Algebra II : Exponents

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Example Questions

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 #481 : Exponents

Evaluate: x^5*2x^2

Possible Answers:

$4x^{10}$

2x^7

4x^8

4x^7

$2x^{10}$

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 #482 : Exponents

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

Possible Answers:

12x^9

12x^5

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

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

$12x^{-14}$

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 #483 : Exponents

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 #484 : Exponents

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

Possible Answers:

x^by^c

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

-x^by^c

$xy^{b-c}$

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

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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Example Question #155 : Simplifying Exponents

Divide: $\frac{a^3c}{a^6b^{-3}c^{-9}}$

Possible Answers:

$\frac{1}{a^3b^3c^{10}}$

$\frac{c^{10}}{a^3b^3}$

$\frac{b^3c^{10}}{a^3}$

$\frac{b^3}{a^3c^{10}}$

$\frac{b^3}{a^3c^8}$

Correct answer:

$\frac{b^3c^{10}}{a^3}$

Explanation:

For the common bases that are divided, the exponents can be subtract from numerator to denominator.

Evaluate the terms.

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

Since there is no term on the numerator, we can assume $b^{0}=1$ .

$\frac{b^{0}}{b^{-3}} = \frac{1}{b^{-3}}= \frac{1}{\frac{1}{b^3}} = b^3$

$\frac{c^1}{c^{-9}} = c^{1-(-9)} = c^{10}$

Multiply the three terms together.

$\frac{1}{a^3}\cdot b^3 \cdot c^{10} = \frac{b^3c^{10}}{a^3}$

The answer is: $\frac{b^3c^{10}}{a^3}$

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Example Question #485 : Exponents

Solve: $\frac{4^{500}\times 2^{250}}{8^{125}}$

Possible Answers:

$4^{625}$

$2^{875}$

$2^{630}$

$2^{625}$

Correct answer:

$2^{875}$

Explanation:

To be able to add or subtract exponents, we should change the bases so that every base is common.

Four is two squared, and eight is two cubed. We can rewrite the numbers using base two.

$\frac{4^{500}\times 2^{250}}{8^{125}}=\frac{2^{2(500)}\times 2^{250}}{2^{3(125)}}= \frac{2^{1000}\times 2^{250}}{2^{375}}$

When exponents of the same bases are multiplied, the powers can be added. When exponents of the same base are divided, their powers can be subtracted.

$2^{1000+250-375} = 2^{875}$

The answer is: $2^{875}$

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Algebra II : Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #150 : Multiplying And Dividing Exponents

Example Question #481 : Exponents

Example Question #482 : Exponents

Example Question #483 : Exponents

Example Question #484 : Exponents

Example Question #155 : Multiplying And Dividing Exponents

Example Question #156 : Multiplying And Dividing Exponents

Example Question #157 : Multiplying And Dividing Exponents

Example Question #155 : Simplifying Exponents

Example Question #485 : Exponents

All Algebra II Resources

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