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ISEE Upper Level Math : Numbers and Operations

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 #5 : How To Add Exponents

Simplify:

$x^{6}\cdot x^{4}$

Possible Answers:

$x^{24}$

$x^{2}$

$x^{-2}$

$x^{10}$

$x^{-10}$

Correct answer:

$x^{10}$

Explanation:

When multiplying exponents, the exponents are added together.

$x^{6}\cdot x^{4} = x^{6+4}=x^{10}$

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Example Question #6 : How To Add Exponents

Simplify:

$2x^{2}\cdot 3x^{4}$

Possible Answers:

$6x^{8}$

$\frac{2}{3}x^{6}$

$5x^{6}$

$6x^{2}$

$6x^{6}$

Correct answer:

$6x^{6}$

Explanation:

When multiplying exponents, the exponents are added together.

$2x^{2}\cdot 3x^{4}=6x^{2+4}=6x^{6}$

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Example Question #57 : Exponential Operations

Simplify the expression:

$3x^{4}+6x^{3}-9x^{2}$

Possible Answers:

$3x(x^{2}+3x-3)$

$3x^{2}(x^{2}+2x-3)$

$3x^{2}(x^{2}+2x-3x)$

$2x^{2}(x^{2}+2x-3x)$

$3x(x^{2}+2x-3)$

Correct answer:

$3x^{2}(x^{2}+2x-3)$

Explanation:

To simplify this problem we need to factor out a 3x^2

$3x^{4}+6x^{3}-9x^{2}$

$=3x^{2}(x^{2}+2x-3)$

We can do this because multiplying exponents is the same as adding them. Therefore,

$=3x^{2}(x^{2}+2x-3)$

$=3x^2 \cdot x^2 +3x^2\cdot2x -3x^2\cdot3=3x^{2+2}+3\cdot2x^{2+1}-3\cdot 3x^2$

=3x^4+6x^3-9x^2

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Example Question #111 : Numbers And Operations

Solve: $3^5 \cdot 3^{-8}$

Possible Answers:

$3^{13}$

$\frac{1}{3^{13}}$

$\frac{1}{9}$

$\frac{1}{27}$

Correct answer:

$\frac{1}{27}$

Explanation:

It is not necessary to evaluate both terms and multiply.

According to the rules of exponents, when we have the same bases raised to some power that are multiplied with each other, we can add the powers.

$3^5 \cdot 3^{-8} = 3^{5+( -8)} = 3^{-3}$

This term can be rewritten as a fraction.

$3^{-3 } = \frac{1}{3^3} = \frac{1}{27}$

The answer is: $\frac{1}{27}$

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Example Question #7 : How To Add Exponents

Which of the following is equivalent to the expression below?

$4^{x}\cdot2^{5}$

Possible Answers:

$6^{5x}$

$8^{5x}$

$2^{2x+5}$

$8^{10x}$

Correct answer:

$2^{2x+5}$

Explanation:

When exponents are multiplied by one another, and the base is the same, the exponents can be added together.

The first step is to try to create a common base.

$4^{x}\cdot2^{5}$

Given that the square of 2 is for, the expression can be rewritten as:

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

$2^{2x+5}$

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Example Question #62 : Exponential Operations

Simplify:

$(6a^3)(\frac{1}{3}a^2)$

Possible Answers:

2a^5

2a^6

a^5

a^6

2a^4

Correct answer:

2a^5

Explanation:

Based on the product rule for exponents in order to multiply two exponential terms with the same base, add their exponents:

$(x)^a(x)^b=x^{a+b}$

So we can write:

$(6a^3)\left(\frac{1}{3}a^2\right)=\left(\frac{6}{3}\right)\times a^{3+2}=2a^5$

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All ISEE Upper Level Math Resources

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

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ISEE Upper Level Math : Numbers and Operations

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #5 : How To Add Exponents

Example Question #6 : How To Add Exponents

Example Question #57 : Exponential Operations

Example Question #111 : Numbers And Operations

Example Question #7 : How To Add Exponents

Example Question #62 : Exponential Operations

All ISEE Upper Level Math Resources

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