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ISEE Upper Level Math : Variables and Exponents

Study concepts, example questions & explanations for ISEE Upper Level Math

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All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1021 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify:

$\frac{(2xy)^{6}}{2x^{2} y^{8}}$

Possible Answers:

$32 x^{4} y^{2}$

$\frac{32 x^{4} }{ y^{2}}$

$\frac{32 }{ x^{4}y^{2}}$

$\frac{32y^{2} }{ x^{4}}$

Correct answer:

$\frac{32 x^{4} }{ y^{2}}$

Explanation:

$\frac{(2xy)^{6}}{2x^{2} y^{8}}$

$= \frac{2^{6} \cdot x^{6}y^{6}}{2x^{2} y^{8}}$

$= \frac{64 x^{6-2}}{2 y^{8-6}}$

$= \frac{32 x^{4} }{ y^{2}}$

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Example Question #1021 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Divide the following:

$x^8 \div x^2$

Possible Answers:

$x^{10}$

x^4

x^3

x^6

x^2

Correct answer:

x^6

Explanation:

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

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

Now, let’s combine the following:

$x^8 \cdot x^2 = x^{8-2}$

$x^8 \cdot x^2 = x^{6}$

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Example Question #1022 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Divide the following:

$\frac{a^2 b^4}{a b^2}$

Possible Answers:

ab^2

a^3b

a^2b

a^3b^6

Correct answer:

ab^2

Explanation:

When dividing variables, we can only divide like variable.

Also, when dividing variables with exponents, we subtract the exponents. In other words:

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

So, we get

$\frac{a^2 b^4}{a b^2}$

$\frac{a^2b^4}{a^1b^2}$

$a^{2-1}b^{4-2}$

a^1b^2

ab^2

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Example Question #1021 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify:

$y^{12} \div y^2$

Possible Answers:

y^6

y^4

y^8

$y^{14}$

$y^{10}$

Correct answer:

$y^{10}$

Explanation:

To simplify, we will use the following formula:

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

So, given the problem, we get

$y^{12} \div y^2 = y^{12-2}$

$y^{12} \div y^2 = y^{10}$

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Example Question #1022 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Divide the following:

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

Possible Answers:

$h^{12}$

h^5

$h^{20}$

h^8

h^1

Correct answer:

h^8

Explanation:

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

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

So, we get

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

$h^{10-2}$

h^8

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Example Question #1023 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Divide the following:

$\frac{y^9}{y^3}$

Possible Answers:

2y^2

y^2

y^6

y^3

y^8

Correct answer:

y^6

Explanation:

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

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

So, we get

$\frac{y^9}{y^3} = y^{9-3}$

$\frac{y^9}{y^3} = y^6$

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Example Question #1024 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Divide the following::

$p^9 \div p^3$

Possible Answers:

$p^{12}$

p^6

$p^{93}$

p^3

p^1

Correct answer:

p^6

Explanation:

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

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

Now, let’s divide the following:

$p^9 \div p^3 = p^{9-3}$

$p^9 \div p^3 = p^{6}$

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Example Question #1025 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Solve the following:

$\frac{18x^4}{9x}$

Possible Answers:

2x^4

9x^3

2x^3

9x^2

Correct answer:

2x^3

Explanation:

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

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

Also, we divide the coefficients like normal.

So, we get

$\frac{18x^4}{9x}$

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

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

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

$2x^{4-1}$

2x^3

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Variables and Exponents

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1021 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1021 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1022 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1021 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1022 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1023 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1024 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1025 : Isee Upper Level (Grades 9 12) Mathematics Achievement

All ISEE Upper Level Math Resources

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