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Questions and Answers
Which of the following is equivalent to $\frac{x^5y^2}{xy^2}$ when $x$ does not equal 0, and $y$ does not equal 0?
Which of the following is equivalent to $\frac{x^5y^2}{xy^2}$ when $x$ does not equal 0, and $y$ does not equal 0?
- x^3
- y^2
- x^2
- x^4 (correct)
Which expression is not equal to 125?
Which expression is not equal to 125?
- 5(5^{3/2}/5)^2 (correct)
- 125
- 25
- 5^3
A fraction reduces to 36. If its denominator is $6x^5$, what is its numerator?
A fraction reduces to 36. If its denominator is $6x^5$, what is its numerator?
6^3x^5
What is the correct simplification of $\frac{5.4 \times 10^{12}}{1.2 \times 10^3}$ written in scientific notation?
What is the correct simplification of $\frac{5.4 \times 10^{12}}{1.2 \times 10^3}$ written in scientific notation?
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Which of the following statements is not true regarding operations with exponents?
Which of the following statements is not true regarding operations with exponents?
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Study Notes
Equivalent Expressions
- The expression ( \frac{x^5y^2}{xy^2} ) simplifies to ( x^{4} ) when ( x \neq 0 ) and ( y \neq 0 ).
Non-Equivalent Expressions
- The expression ( 5\left(\frac{5^3}{2 \cdot 5}\right)^2 ) does not equal 125.
Reducing Fractions
- A fraction that reduces to 36 with a denominator of ( 6x^5 ) has a numerator of ( 6^3x^5 ).
Scientific Notation
- The simplification of ( \frac{5.4 \times 10^{12}}{1.2 \times 10^{3}} ) in scientific notation results in ( 4.5 \times 10^{9} ).
Operations with Exponents
- It is incorrect to state that to subtract powers with the same base, one should divide the exponents; the correct operation is to subtract the exponents.
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