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ISEE Upper Level Math : How to multiply exponential variables

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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

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Example Question #111 : Variables

Combine the following:

$x^3 \cdot x^7$

Possible Answers:

$2x^{10}$

$x^{37}$

$x^{21}$

x^4

$x^{10}$

Correct answer:

$x^{10}$

Explanation:

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

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

Now, let’s combine the following:

$x^3 \cdot x^7 = x^{3+7}$

$x^3 \cdot x^7 = x^{10}$

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Example Question #112 : Variables

Combine the following:

$a^5 \cdot b^2 \cdot a^7 \cdot b^4$

Possible Answers:

$a^{12} \cdot b^6$

$a^{35} \cdot b^8$

$ab^{18}$

$2a^{12} \cdot 2b^6$

$ab^{43}$

Correct answer:

$a^{12} \cdot b^6$

Explanation:

When combining variables with exponents, we can only combine like variables.

When multiply variables with exponents, we add the exponents. In other words:

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

So, we get

$a^5 \cdot b^2 \cdot a^7 \cdot b^4$

$a^5 \cdot a^7 \cdot b^2 \cdot b^4$

$a^{5+7} \cdot b^{2+4}$

$a^{12} \cdot b^6$

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Example Question #21 : How To Multiply Exponential Variables

Simplify:

$b^2 \cdot b^7$

Possible Answers:

b^5

b^9

$b^{14}$

$b^{27}$

b^7

Correct answer:

b^9

Explanation:

To simplify, we will use the following formula:

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

So, given the problem, we get

$b^2 \cdot b^7 = b^{2+7}$

$b^2 \cdot b^7 = b^9$

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Example Question #114 : Variables

Combine the following:

$b^4 \cdot b^5 \cdot b$

Possible Answers:

3b^9

b^9

$b^{20}$

$3b^{10}$

$b^{10}$

Correct answer:

$b^{10}$

Explanation:

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

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

So, we get

$b^4 \cdot b^5 \cdot b$

$b^4 \cdot b^5 \cdot b^1$

$b^{4+5+1}$

$b^{10}$

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Example Question #1001 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify the following expression:

(4x^2)^3+6x^6

Possible Answers:

18x^6

64x^5+6x^6

70x^6

64x^4-6x^6

Correct answer:

70x^6

Explanation:

Simplify the following expression:

(4x^2)^3+6x^6

Let's begin with the first term.

Because we are raising the whole part to the third, we need to cube each piece, the 4 and the x squared.

4^3(x^2)^3+6x^6=64x^6+6x^6

Next, simply add our two terms to get our answer

64x^6+6x^6=70x^6

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Example Question #1011 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Multiply the following:

$x^5 \cdot x^2$

Possible Answers:

$x^{10}$

$2x^{10}$

2x^7

x^7

$2x^{12}$

Correct answer:

x^7

Explanation:

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

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

So, we get

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

$x^5 \cdot x^2 = x^7$

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Example Question #311 : Algebraic Concepts

Multiply the following:

$b^4 \cdot b^2$

Possible Answers:

$b^{42}$

b^2

b^6

b^8

b^4

Correct answer:

b^6

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:

$b^4 \cdot b^2 = b^{4+2}$

$b^4 \cdot b^2 = b^{6}$

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Example Question #1013 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Solve the following:

$3y^3 \cdot 4y^2$

Possible Answers:

12y^6

7y^6

12y^5

7y^5

12y

Correct answer:

12y^5

Explanation:

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

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

Also, we will multiply coefficients like normal.

So, we get

$3y^3 \cdot 4y^2$

$12(y^3 \cdot y^2)$

$12(y^{3+2})$

12y^5

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Example Question #121 : Variables

Simplify the following expression:

(9x^5y^2)(12x^3y^8)

Possible Answers:

$108x^{15}y^{10}$

$108x^8y^{10}$

$98x^8y^{10}$

$108x^{10}y^{24}$

$108x^8y^{16}$

Correct answer:

$108x^8y^{10}$

Explanation:

Simplify the following expression:

(9x^5y^2)(12x^3y^8)

To combine these, we need to multiply our coefficients and our variables.

First, multiply the coefficients

9*12=108

Next, multiply our variables by adding the exponent:

$(x^5y^2)(x^3y^8)=x^{5+3}y^{2+8}=x^8y^{10}$

So, we put it all together to get:

$108x^8y^{10}$

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : How to multiply exponential variables

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #111 : Variables

Example Question #112 : Variables

Example Question #21 : How To Multiply Exponential Variables

Example Question #114 : Variables

Example Question #1001 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1011 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #311 : Algebraic Concepts

Example Question #1013 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #121 : Variables

All ISEE Upper Level Math Resources

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