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Algebra 1 : Monomials

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Example Question #43 : How To Multiply Monomial Quotients

Choose the answer that is equal to $4x^{2}12x^{-8}$ .

Possible Answers:

$48x^{-16}$

$12x^{-16}$

$48x^{-6}$

$-48x^{16}$

Correct answer:

$48x^{-6}$

Explanation:

First multiply 4 and 12 to get the expression

$48x^{2}x^{-8}$ .

Then remember that to multiple like terms with exponents, add the exponents.

This gives the answer, $48x^{-6}$ .

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Example Question #45 : How To Multiply Monomial Quotients

Choose the expression that is equal to $4z^{-6}z^{4}$ .

Possible Answers:

$4z^{-24}$

$4z^{10}$

$4/z^{2}$

$16z^{-2}$

Correct answer:

$4/z^{2}$

Explanation:

Remember that to multiply like variables with exponents you add the exponents.

This gives $4z^{-2}$ .

Also remember that a variable raised to a negative exponential is the same as 1/that same variable to that positive exponential.

For example, $z^{-2}$ is equivalent to $1/z^{2}$ .

This thinking leads to the answer $4/z^{2}$ .

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Example Question #46 : How To Multiply Monomial Quotients

Multiply: $\frac{2y}{3x}\cdot \frac{6x^2}{8y^3}$

Possible Answers:

$\frac{x}{2y^2}$

$\frac{12x^2+y}{24y^3+x}$

$\frac{x}{12y^2}$

$\frac{11x}{12y^2}$

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

Correct answer:

$\frac{x}{2y^2}$

Explanation:

Write out the factors of the second term to see what terms can be cancelled in the numerator and denominator.

$\frac{2y}{3x}\cdot \frac{6x^2}{8y^3}= \frac{2y}{3x}\cdot \frac{2\cdot 3\cdot x\cdot x}{2\cdot 2\cdot 2\cdot y\cdot y\cdot y}$

After cancellation of common terms, the answer is: $\frac{x}{2y^2}$

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Example Question #47 : How To Multiply Monomial Quotients

Simplify the expression $\frac{(xy^{2})^{4} \cdot x }{y}$ . What is the degree of the simplified monomial?

Possible Answers:

Correct answer:

Explanation:

$\frac{(xy^{2})^{4} \cdot x }{y}$

$= \frac{x^{1} \cdot x^{4} \cdot (y^{2})^{4}}{y}$

$= \frac{ x^{1+ 4} \cdot (y^{2\cdot 4}) }{y}$

$= \frac{ x^{5} y^{8} }{y^{1}}$

$= x^{5} y^{8- 1}$

$= x^{5} y^{7}$

The degree of a monomial term is the sum of its exponents, which here is

5+7 = 12 .

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Example Question #571 : Variables

Simplify the expression $\frac{(xy^{2})^{4} \cdot x }{y}$ . What is the exponent of ?

Possible Answers:

Correct answer:

Explanation:

$\frac{(xy^{2})^{4} \cdot x }{y}$

$= \frac{x^{1} \cdot x^{4} \cdot (y^{2})^{4}}{y}$

$= \frac{ x^{1+ 4} \cdot (y^{2\cdot 4}) }{y}$

$= \frac{ x^{5} y^{8} }{y^{1}}$

$= x^{5} y^{8- 1}$

$= x^{5} y^{7}$

The exponent of is 7.

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Example Question #151 : Monomials

Simplify: $\frac {(x^{2}y)^{3}}{ (xy)^{4}}$ .

What is the exponent of in the simplified form, and does it appear in the numerator or denominator?

Possible Answers:

2, in the numerator

does not appear in the simplified form of the expression

2, in the denominator

1, in the numerator

1, in the denominator

Correct answer:

1, in the denominator

Explanation:

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

$=\frac {(x^{2})^{3} \cdot y ^{3}}{ x^{4} \cdot y^{4}}$

$=\frac {x^{2 \cdot 3 }\cdot y ^{3}}{ x^{4} \cdot y^{4}}$

$=\frac {x^{6 }\cdot y ^{3}}{ x^{4} \cdot y^{4}}$

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

$=\frac {x^{2}}{ y^{1}}$

The exponent of is 1, in the denominator.

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Example Question #41 : How To Multiply Monomial Quotients

Simplify: $\frac {(x^{2}y)^{3}}{ (xy)^{4}}$ .

What is the exponent of in the simplified form, and does it appear in the numerator or denominator?

Possible Answers:

2, in the denominator

1, in the numerator

2, in the numerator

1, in the denominator

does not appear in the simplified form of the expression

Correct answer:

2, in the numerator

Explanation:

To simplify this expression use the law of exponents which state that when a term is raised to a power, multiply the exponents. Also, when terms of like bases are divided the exponents are subtracted.

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

$=\frac {(x^{2})^{3} \cdot y ^{3}}{ x^{4} \cdot y^{4}}$

$=\frac {x^{2 \cdot 3 }\cdot y ^{3}}{ x^{4} \cdot y^{4}}$

$=\frac {x^{6 }\cdot y ^{3}}{ x^{4} \cdot y^{4}}$

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

$=\frac {x^{2}}{ y^{1}}$

The exponent of is 2, in the numerator.

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Example Question #151 : Monomials

Simplify the expression

$\frac{(3x^{4})^{2}}{2x^{3}}$ .

What is the coefficient in this expression after it is simplified?

Possible Answers:

$\frac{9}{4}$

$\frac{9}{2}$

Correct answer:

$\frac{9}{2}$

Explanation:

To simplify the expression use the rule of exponents which states that when like bases are raised to a power the exponents are multiplied together. When like bases are divided that means that their exponents are subtracted.

$\frac{(3x^{4})^{2}}{2x^{3}}$

$= \frac{3^{2}(x^{4})^{2}}{2x^{3}}$

$= \frac{9x^{4 \cdot 2}}{2x^{3}}$

$= \frac{9x^{8}}{2x^{3}}$

$= \frac{9}{2} \cdot \frac{x^{8}}{x^{3}}$

$= \frac{9}{2} \cdot x^{8-3}$

$= \frac{9}{2} x^{5}$

The coefficient of this simplified form is $\frac{9}{2}$ .

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Example Question #152 : Monomials

Simplify: $\frac{\sqrt{x} \cdot \sqrt[3]{y}}{x^2y^4}$

Possible Answers:

$\frac{1}{x^{\frac{3}{2}} y^{\frac{11}{3}}}$

$x^{\frac{2}{3}} y^{\frac{3}{11}}$

$\textup{Cannot be reduced any further.}$

$\frac{1}{x^{\frac{2}{3}} y^{\frac{3}{11}}}$

$x^{\frac{3}{2}} y^{\frac{11}{3}}$

Correct answer:

$\frac{1}{x^{\frac{3}{2}} y^{\frac{11}{3}}}$

Explanation:

In order to simplify, rewrite the numerator in terms of exponential powers.

$\frac{\sqrt{x} \cdot \sqrt[3]{y}}{x^2y^4} = \frac{x^{\frac{1}{2}} y^{\frac{1}{3}}}{x^2y^4}$

Because similar bases are divided, subtract the powers of the numerator with the denominator.

$x^{\frac{1}{2}-2}= x^{\frac{1}{2}-\frac{4}{2}} = x^{-\frac{3}{2}}$

$y^{\frac{1}{3}-4} = y^{\frac{1}{3}-\frac{12}{3}} =y^{-\frac{11}{3}}$

Since these two variables have negative exponents, we can simply take the inverse of both to eliminate the negative exponents.

$x^{-\frac{3}{2}} = \frac{1}{x^{\frac{3}{2}}}$

$y^{-\frac{11}{3}} = \frac{1}{y^{\frac{11}{3}}}$

Multiply both fractions.

The answer is: $\frac{1}{x^{\frac{3}{2}} y^{\frac{11}{3}}}$

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Algebra 1 : Monomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #43 : How To Multiply Monomial Quotients

Example Question #45 : How To Multiply Monomial Quotients

Example Question #46 : How To Multiply Monomial Quotients

Example Question #47 : How To Multiply Monomial Quotients

Example Question #571 : Variables

Example Question #151 : Monomials

Example Question #41 : How To Multiply Monomial Quotients

Example Question #151 : Monomials

Example Question #152 : Monomials

All Algebra 1 Resources

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