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High School Math : Distributing Exponents

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Example Questions

Example Question #1 : Simplifying Exponents

$\log_{x}27e^{3}=3$

Solve for .

Possible Answers:

1/2e

Correct answer:

Explanation:

First, set up the equation: x^3=27 e^3 . Simplifying this result gives x = 3 .

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Example Question #1 : Distributing Exponents (Power Rule)

What is the largest positive integer, , such that 2^z is a factor of 16^4 ?

Possible Answers:

Correct answer:

Explanation:

16^4 = (2^4)^4 = 2^1^6 . Thus, is equal to 16.

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Example Question #2 : Simplifying Exponents

Order the following from least to greatest:

$25^{100}$

$2^{300}$

$3^{500}$

$4^{400}$

$2^{600}$

Possible Answers:

$3^{500}, 4^{400}, 2^{300}, 25^{100}, 2^{600}$

$2^{300}, 2^{600}, 3^{500}, 25^{100}, 4^{400}$

$25^{100}, 2^{300}, 2^{600}, 3^{500}, 4^{400}$

$2^{300}, 25^{100}, 2^{600}, 3^{500}, 4^{400}$

$2^{600}, 2^{300}, 25^{100}, 3^{500}, 4^{400}$

Correct answer:

$2^{300}, 25^{100}, 2^{600}, 3^{500}, 4^{400}$

Explanation:

In order to solve this problem, each of the answer choices needs to be simplified.

Instead of simplifying completely, make all terms into a form such that they have 100 as the exponent. Then they can be easily compared.

2^3^0^0 = (2^3)^1^0^0 = 8^1^0^0 , 3^5^0^0 = (3^5)^1^0^0 = 243^1^0^0 , 4^4^0^0 = (4^4)^1^0^0 = 256^1^0^0 , and 2^6^0^0 = (2^6)^1^0^0 = 64^1^0^0 .

Thus, ordering from least to greatest: 8^1^0^0, 25^1^0^0, 64^1^0^0, 243^1^0^0, 256^1^0^0 .

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Example Question #1 : Simplifying Exponents

Simplify the expression:

$(3x^4y^2)(4xy^2)^{-3}$

Possible Answers:

$\frac{3x}{16y^3}$

$\frac{3x}{64y^3}$

$\frac{3x}{64y^4}$

Cannot be simplified

Correct answer:

$\frac{3x}{64y^4}$

Explanation:

Begin by distributing the exponent through the parentheses. The power rule dictates that an exponent raised to another exponent means that the two exponents are multiplied:

$(3x^{4}y^2)(4xy^2)^{-3}= (3xy^2)(4^{-3}x^{-3}y^{-6})$

Any negative exponents can be converted to positive exponents in the denominator of a fraction:

$\frac{3x^4y^2}{64x^3y^6}$

The like terms can be simplified by subtracting the power of the denominator from the power of the numerator:

$\frac{3x^4y^2}{64x^3y^6}=\frac{3}{64}x^{4-3}y^{2-6}=\frac{3}{64}xy^{-4}$

$\frac{3x}{64y^4}$

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High School Math : Distributing Exponents

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Simplifying Exponents

Example Question #1 : Distributing Exponents (Power Rule)

Example Question #2 : Simplifying Exponents

Example Question #1 : Simplifying Exponents

All High School Math Resources

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