\color{red} \textrm{Show Your Work}! You must show your work with enough detail to clearly indicate:
Which exponent law/property you used
That you solved the problem algebraically (with equation-based methods)
Even with the correct answer, responses without enough work will receive no credit.
Finally, when possible, remember that it is best to write polynoials arranging each monomial term with variables in alphabetical order. And the monomials within a polynomials should be listed by descending degree.
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Question 1
1.
Apply the "product rule" to the following expression as a (single) base raised to a (single) power.
q^{-9}q^{3n}
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Question 2
2.
Apply the "quotient rule" to the following expression to generate an equivalent expression.
\frac{x^{6}y^{-2}}{x^{2}y^{3}}
HINT: If you're having trouble, split the problem into two, easier problems by rewriting the expression as a product \frac{h^{m}x^{-3}}{h^{n}x}=\frac{h^{m}}{h^{n}}\cdot \frac{x^{-3}}{x}
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Question 3
3.
Which of the following is equivalent to \big(\frac{1}{2x}\big)^{-3}? Select all that apply.
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Question 4
4.
Evaluate the expression if t=7.
\big(3^{2}x^{t-7}\big)^{2}
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Question 5
5.
Use the laws of exponents to generate a simplified expression.
\frac{(xyz)^{2}}{x^{5}z}
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Question 6
6.
Terrance tries to re-write the expression \big(m^{-3}\cdot m^{2}\big)^{-1}. Here is his work.
Step 0: \big(m^{-3}\cdot m^{2}\big)^{-1}
Step 1: =\big(m^{(-3+2)}\big)^{-1}
Step 2: =\big(m^{-1}\big)^{-1}
Step 3: =-\big(m^{-1}\big)^{1}
Step 4: =-m^{-1}
Step 5: =-\frac{1}{m}
Did Terrance make a mistake? Select all that apply.
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Question 7
7.
Emmy is working through the same problem using a different strategy. Here is her work.
Step 0: \big(m^{-3}\cdot m^{2}\big)^{-1}
Step 1: =\frac{1}{m^{-3}\cdot m^{2}}
Step 2: =\frac{1}{m^{(-3+2)}}
Step 3: =\frac{1}{m^{-1}}
Step 4: =\frac{m^{0}}{m^{-1}}
Step 5: =m^{(0--1)}
Step 6: =m^{1}
Which statement best describes Emmy's accuracy?
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Question 8
8.
Use the laws of exponents to simplify the expression.
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1
Question 9
9.
Use the laws of exponents to simplify the expression.