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College Algebra : Review and Other Topics

Study concepts, example questions & explanations for College Algebra

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Example Questions

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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Example Question #1 : Distributing Exponents (Power Rule)

Simplify:

(4x^3)^4

Possible Answers:

16x^7

$256x^{12}$

4x^7

512x

$4x^{12}$

Correct answer:

$256x^{12}$

Explanation:

Use the power rule to distribute the exponent:

$(4x^3)^4\rightarrow 4^4\cdot x^{3\cdot 4}\rightarrow 256x^{12}$

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Example Question #1 : Review And Other Topics

Simplify the following expression:

(9x^6y^2z^5)^2

Possible Answers:

$81x^{8}y^4z^{7}$

$18x^{12}y^4z^{10}$

$11x^{12}y^4z^{10}$

$81x^{12}y^4z^{10}$

Correct answer:

$81x^{12}y^4z^{10}$

Explanation:

Simplify the following expression:

(9x^6y^2z^5)^2

To raise exponents to another power, we need to multiply them:

$(9x^6y^2z^5)^2=9^2x^{6*2}y^{2*2}z^{5*2}=81x^{12}y^4z^{10}$

So we get:

$81x^{12}y^4z^{10}$

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Example Question #1 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Simplify.

$(x^4)^{6}$

Possible Answers:

$x^{24}$

x^2

$x^{10}$

$x^{-2}$

$x^{46}$

Correct answer:

$x^{24}$

Explanation:

When an exponent is being raised by another exponent, we just multiply the powers of the exponents and keep the base the same.

$(x^4)^{6}=x^{4*6}=x^{24}$

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Example Question #21 : Distributing Exponents (Power Rule)

Simplify.

$(\frac{x^5}{y^3})^3$

Possible Answers:

$\frac{x^{15}}{y^{13}}$

$\frac{x^{15}}{y^3}$

$\frac{x^{8}}{y^6}$

$\frac{x^{15}}{y^9}$

$\frac{x^{15}}{y^8}$

Correct answer:

$\frac{x^{15}}{y^9}$

Explanation:

When an exponent is being raised by another exponent, we just multiply the powers of the exponents and keep the base the same.

$(\frac{x^5}{y^3})^{3}=\frac{x^{5*3}}{y^{3*3}}=\frac{x^{15}}{y^{9}}$

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Example Question #2 : Review And Other Topics

Combine the following terms:

5x^4*3t^3*8x^3

Possible Answers:

120x^7t^3

16x^7t^3

$120x^{36}$

$120x^{10}$

Correct answer:

120x^7t^3

Explanation:

Combine the following terms:

5x^4*3t^3*8x^3

We need to multiply three terms together. We should recognize that the t must be left alone, because it cannot be combined with the x's.

First, multiply all three coefficients

5*3*8=120

Next, combine the x's. Because we are multiplying, we will add the exponents.

x^4*x^3=x^7

Now, put it all together to get:

120x^7t^3

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Example Question #2 : Review And Other Topics

Evaluate

X^7/X^4

Possible Answers:

$X^{28}$

$X^{-3}$

$X^{7/4}$

7/4X

X^3

Correct answer:

X^3

Explanation:

When common variables with exponents are divided, the exponents are subtracted.

$X^7/X^4 = X^{7-4} = X^3$

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Example Question #3 : Review And Other Topics

Evaluate

X^8*X^6

Possible Answers:

14X

$X^{2}$

$X^{48}$

$X^{14}$

48X

Correct answer:

$X^{14}$

Explanation:

When like terms with exponents are multiplied, you add the exponents.

$X^8*X^6 = X^{8+6} = X^{14}$

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Example Question #3 : Review And Other Topics

Evaluate the following:

$x^{2}*x^{4}=$

Possible Answers:

$x^{6}$

$x^{8}$

$2x^{4}$

$x^{2}$

Correct answer:

$x^{6}$

Explanation:

When similar terms raised to n are multiplied, simply add the exponents. Thus

$x^{2}*x^{4}=x^{2+4}=x^{6}$

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Example Question #4 : Review And Other Topics

$x^{3}*x^{5}=$

Possible Answers:

$x^{2}$

$x^{15}$

15x

$x^{5}$

$x^{8}$

Correct answer:

$x^{8}$

Explanation:

When similar terms raised to n are multiplied, simply add the exponents. Thus

$x^{3}*x^{5}=x^{3+5}=x^{8}$

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College Algebra : Review and Other Topics

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #1 : Simplifying Exponents

Example Question #1 : Distributing Exponents (Power Rule)

Example Question #1 : Review And Other Topics

Example Question #1 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Example Question #21 : Distributing Exponents (Power Rule)

Example Question #2 : Review And Other Topics

Example Question #2 : Review And Other Topics

Example Question #3 : Review And Other Topics

Example Question #3 : Review And Other Topics

Example Question #4 : Review And Other Topics

All College Algebra Resources

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