Questions and Answers
What is the simplified form of the expression ( \frac{2x^3}{18x^5} )?
What is the simplified product of ( \frac{2}{5}x^3 \cdot -\frac{3}{10}x^2 )?
-\frac{30}{2}x^2
Find the simplified product where ( x > 0 ): ( \frac{5x}{\sqrt{8x^2 - \sqrt{x}}} ).
( \frac{2x}{10x - \frac{2x}{5}} )
Multiply: ( \frac{4x^3}{4x^2} \cdot (2, \frac{3}{32}x^2 - \frac{x^3}{2x}) ).
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What is the result of ( \left(\frac{10 + 2}{8}\right) \left(\frac{10 - 2}{8}\right) )?
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Simplify the expression ( \left(\frac{2x^3 + 12x}{(2/10)x^5 + (6/x^2)}\right) ).
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Rewrite the expression ( \frac{6}{x} \cdot \frac{4}{y^3} ) using rational exponents.
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Study Notes
Multiplying Radicals and Simplifying Expressions
- Expression: ( \frac{\sqrt{2x^3}}{18x^5} ) simplifies to ( \frac{6x^4}{3x^4} ).
- The greatest common factor is key for simplifying fractions involving radicals.
Finding Simplified Products
- To simplify ( \frac{2}{5}x^3 \left(-\frac{3}{10}x^2\right) ):
- Result: ( -\frac{30x^5}{2x} ).
- Further simplification gives ( -4x^4 ).
Evaluating Radical Products
- For ( \sqrt{5x} \left(\sqrt{8x^2} - \sqrt{x}\right) ) with ( x > 0 ):
- Result: ( \frac{2x}{10x} - \frac{2x}{5} ).
- Simplifies to two distinct fractions when distributing.
Multiplying Complex Expressions
- Combining fractions and radicals in ( \frac{4x^3}{4x^2} \left(2, \frac{3}{32}x^2 - \frac{x^3}{2x}\right) ):
- Result: ( \frac{32x^2}{3} - 8x^3 ).
- Requires careful distribution and combining like terms.
Rational Expression Operations
- For the operation ( \left(\frac{\sqrt{10} + \frac{2}{8}}{\sqrt{10} - \frac{2}{8}}\right) ), results in:
- Final outcome: -22.
- Conjugates may be utilized for rationalizing the denominator.
Working with Mixed Fractions and Radicals
- Expression ( \left(\frac{\sqrt{2x^3} + \frac{12x}}{2}\right) \left(\frac{2}{10x^5} + \frac{6x^2}{12}\right) ):
- Final calculation yields ( \frac{4x^4}{5} + \frac{2x^2}{3x} + \frac{4x^3}{30} + \frac{6x}{2x} ).
- Simplification involves considering the coefficients and common factors.
Rewriting with Rational Exponents
- Rewrite ( \frac{6}{x} \cdot \frac{4}{y^3} ) as:
- Result: ( \frac{x^2}{12} \cdot \frac{y^9}{12} ).
- Common denominator factors are essential for clear expression of results.
Studying That Suits You
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Description
Test your understanding of multiplying radicals with this set of flashcards. Each card provides a mathematical expression to simplify, helping you master radical multiplication techniques. Perfect for students looking to reinforce their knowledge in algebra.
