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ISEE Upper Level Math : Exponential Operations

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Example Questions

Example Question #51 : Exponential Operations

Simplify the following expression:

$\frac{16r^{19}}{8r^6}$

Possible Answers:

$2r^{13}$

$8r^{13}$

2r^5

$2r^{\frac{19}{6}}$

Correct answer:

$2r^{13}$

Explanation:

Simplify the following expression:

$\frac{16r^{19}}{8r^6}$

To solve this question, we need to recall that when dividing exponents we subtract them.

When dividing coefficients, we treat them as regular division.

In this case, we can break up our question into two parts:

$\frac{16r^{19}}{8r^6}\rightarrow\frac{16}{8} \frac{r^{19}}{r^6}$

The coefficients will simply reduce to "2", because 16 divided by 8 is two

The r's are another story. We subtract, so we will get the following:

$\frac{r^{19}}{r^6}=r^{19-6}=r^{13}$

So, if we put our two parts back together, we get:

$2r^{13}$

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Example Question #52 : Exponential Operations

Simplify the following:

$\frac{18t^6u^{14}}{6t^3u^{12}}$

Possible Answers:

3t^3u^3

3t^2u^2

3t^3u^2

12t^3u^2

Correct answer:

3t^3u^2

Explanation:

Simplify the following:

$\frac{18t^6u^{14}}{6t^3u^{12}}$

Let's begin by recalling that when dividing variables with similar base, we need to subtract the exponents.

To deal with the coefficients, simply treat them as a fraction and simplify.

$\frac{18t^6u^{14}}{6t^3u^{12}}=\frac{18}{6}t^{6-3}u^{14-12}=3t^3u^2$

So our answer is

3t^3u^2

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Example Question #51 : Exponential Operations

Simplify the expression:

$6x^{4} + 8x^{3} - 4x^{2}$

Possible Answers:

$10x^{5}$

$10x^{9}$

$2x^{2}(3x^{2}+4x-2)$

$6x^{4} + 4x^{5}$

$6x^{4} + 4x$

Correct answer:

$2x^{2}(3x^{2}+4x-2)$

Explanation:

$6x^{4} + 8x^{3} - 4x^{2}$

$=2x^{2}(3x^{2}+4x-2)$

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Example Question #2 : How To Add Exponents

Simplify:

4x^2+8x^3+16x^2+4x^3

Possible Answers:

4x^2(5+3x^2)

4x^2(5+3x)

x^2(5+3x)

4x^2(5+x)

4x(5+3x)

Correct answer:

4x^2(5+3x)

Explanation:

In order to add exponential terms, both the base and the exponent must be the same. So we can write:

4x^2+8x^3+16x^2+4x^3=(4x^2+16x^2)+(8x^3+4x^3)

=20x^2+12x^3=4x^2(5+3x)

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Example Question #3 : How To Add Exponents

Evaluate:

$\frac{x^0+y^0+1}{x^0-y^0-1}$

Possible Answers:

Correct answer:

Explanation:

Based on the zero-exponent rule we have:

a^0=1

That means any non-zero number raised to the zero power is equal to . So we can write:

$\frac{1+1+1}{1-1-1}=\frac{3}{-1}=-3$

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Example Question #3 : How To Add Exponents

What is the value of the expression:

$x^{3}\cdotx^{y}\cdot x^{2+y}$

Possible Answers:

$x^{4}\cdotx^{y+4}$

$x^{3}\cdotx^{y+2}$

$x^{4}\cdotx^{y+2}$

$x^{6}\cdotx^{y+2}$

Correct answer:

$x^{4}\cdotx^{y+2}$

Explanation:

When values, having the same base, are multiplied by one another, the exponents are added together and the base stays the same.

Thus,

$x^{3}\cdotx^{y}\cdot x^{2+y}$

is equal to

$x^{4}\cdotx^{y+2}$

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Example Question #4 : How To Add Exponents

Simplify: $x^{7}\cdot2x^{3}$

Possible Answers:

$x^{10}$

$x^{21}$

$2x^{21}$

$2x^{10}$

Correct answer:

$2x^{10}$

Explanation:

When multiplying exponents, the exponents are added together. Thus, 3 and 7 are added together for a sum of 10. In this problem, the "2" becomes a coefficient in front of the x. Therefore, the correct answer is:

$2x^{10}$

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Example Question #5 : How To Add Exponents

Simplify:

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

Possible Answers:

$x^{24}$

$x^{2}$

$x^{10}$

$x^{-2}$

$x^{-10}$

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:

$6x^{2}$

$6x^{8}$

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

$5x^{6}$

$6x^{6}$

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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ISEE Upper Level Math : Exponential Operations

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #51 : Exponential Operations

Example Question #52 : Exponential Operations

Example Question #51 : Exponential Operations

Example Question #2 : How To Add Exponents

Example Question #3 : How To Add Exponents

Example Question #3 : How To Add Exponents

Example Question #4 : How To Add Exponents

Example Question #5 : How To Add Exponents

Example Question #6 : How To Add Exponents

Example Question #57 : Exponential Operations

All ISEE Upper Level Math Resources

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