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Questions and Answers
What is the simplified form of the expression $\frac{-2ab^2b^4}{4ab^{-8}}$?
What is the simplified form of the expression $\frac{-2ab^2b^4}{4ab^{-8}}$?
- 1
- - rac{1}{2}ab^{10}
- 2a^3b^{10} (correct)
- -a^2b^{10} (correct)
What is the simplified form of the expression $\frac{3a^2b^{-4}}{12a^{-2}b^{-2}}$?
What is the simplified form of the expression $\frac{3a^2b^{-4}}{12a^{-2}b^{-2}}$?
- \frac{1}{4}a^4b^2 (correct)
- 4a^4b^2 (correct)
- 3a^{-4}b^{-2}
- 1
What is the simplified form of the expression $\frac{a^{2}b^{-3}}{a^{-2}b^{2}}$?
What is the simplified form of the expression $\frac{a^{2}b^{-3}}{a^{-2}b^{2}}$?
- 1
- a^{4}b^{-1} (correct)
- a^{4}b^{-5} (correct)
- a^{4}b^{5}
What are the values of $x$, $y$, and $z$ in the expression $[(x^2y^3)^{-1} (x^{-2}y^{2}z)^{2}]^{2}$ if $x \neq 0$, $y \neq 0$, $z \neq 0$?
What are the values of $x$, $y$, and $z$ in the expression $[(x^2y^3)^{-1} (x^{-2}y^{2}z)^{2}]^{2}$ if $x \neq 0$, $y \neq 0$, $z \neq 0$?
What error did Tamika make in her simplification of $\frac{18a^{-5} b^{-6}}{30a^{3}b^{-5}}$?
What error did Tamika make in her simplification of $\frac{18a^{-5} b^{-6}}{30a^{3}b^{-5}}$?
How would you simplify the expression $\left(\frac{20x^{5}y^{2}}{5x^{-3}y^{7}}\right)^{-3}$?
How would you simplify the expression $\left(\frac{20x^{5}y^{2}}{5x^{-3}y^{7}}\right)^{-3}$?
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Study Notes
Simplifying Rational Expressions Study Notes
- Simplifying involves expressing answers with positive exponents.
- Key example: (-2ab^2b^4/4ab^{-8}) simplifies to (\frac{1}{8}ab^6) when (a \neq 0) and (b \neq 0).
Additional Examples of Simplification
- Example: (\frac{3a^2b^{-4}}{12a^{-2}b^{-2}}) reduces to (\frac{1}{16}ab^2) under the condition (a \neq 0) and (b \neq 0).
- For (\frac{a^2b^{-3}}{a^{-2}b^2}), the result is (a^4b^{-5}) or (\frac{a^4}{b^5}) where (a \neq 0) and (b \neq 0).
Complex Expression Simplification
- Expression: ([(x^2y^3)^{-1}(x^{-2}y^2z)^2]^2) with conditions (x \neq 0), (y \neq 0), (z \neq 0) simplifies to:
- (x^4) as the numerator
- (y^{14}) and (z^4) as denominators.
Identifying Errors in Simplification
- Common error illustrated by Tamika: misadding exponents instead of correctly applying the laws of exponents.
- Example error: (\frac{18a^{-5}b^{-6}}{30a^3b^{-5}} = \frac{3}{5}a^2b^{11}) is inaccurate due to exponent miscalculation.
Steps for Proper Simplification
- When simplifying ((\frac{20x^5y^2}{5x^{-3}y^7})^{-3}):
- First, divide coefficients and adjust base exponents (use subtraction).
- Raise the entire result to the (-3) power.
- Ensure all exponents are positive in the final expression.
- Use properties like power of a power and simplifying exponent expressions to maintain correct results.
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