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Algebra 1 : Variables

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Example Question #581 : Variables

Simplify the expression

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

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

Possible Answers:

$\frac{9}{2}$

$\frac{9}{4}$

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 #582 : Variables

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

Possible Answers:

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

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

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

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

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

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 : Variables

Study concepts, example questions & explanations for Algebra 1

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Example Question #581 : Variables

Example Question #582 : Variables

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