Algebra LS-2 Quiz v2

Nota Bene
\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 polynomials arranging each monomial term with variables in alphabetical order. And the monomials within a polynomials should be listed by descending degree.

Select all the pairs of equivalent expressions.

Select all the expressions with a value less than 1.

How would you write 12^{-3} using only positive exponents?

How would you rewrite \frac{1}{256^{-4}} using only positive exponents?

Select all the expressions that are equivalent to 3^{4}\div 3^{9} = \frac{3^{4}}{3^{9}}

Is 5(\frac{1}{5^{3}})=5(5^{3}) ? Choose the option that best explains the correct answer.

Which of the following is equivalent to 12^{3}\cdot 12^{9}\cdot 12^{4}\cdot 12^{2} ?

Use the laws of exponents to write an equivalent expression that is maximally concise.
7q^{2}r^{1}\cdot 4q^{-3}r^{2}

Use the laws of exponents to write an equivalent expression that is maximally concise.
\frac{(\frac{1}{2})^{-1}a^{2}b^{-2}c^{5}}{a^{2}b^{-3}c^{2}}

Use the laws of exponents to write an equivalent expression that is maximally concise.
(\frac{3m^{2}n^{7}}{m})^{5}

Stephen King is a famously prolific writer, having published over 60 novels and 200 short stories. If King wrote 10^{7} words during a period of 10^{3} days, what was his average rate of composition in \frac{\textrm{words}}{\textrm{day}} ?

Multiply:

(2x^{3}+\frac{4}{7}x^{2})(x-14)

Every degree-2 polynomial in one variable can be expressed as ax^{2}+bx^{1}+cx^{0} \textrm{, where } a, b, c \in \mathbb{R} \textrm{ and } a\neq0

Create an example where multiplying two, degree 2 polynomials does not yield another degree 2 polynomial.

Is the set of polynomials in one variable closed under multiplication? Explain your reasoning.

HINT: Think about how we multiply polynomials by using complicated versions (technically, "corollaries") of the distributive property. If both the things we start with are polynomials, is it possible that the product (the answer) is not another polynomial of some sort?

Note: Make sure you type enough here to make your thinking clear. Grading for this question will go by the quality of the explanation more than the accuracy of the answer.

Select all the pairs of equivalent expressions.

Select all the expressions with a value less than 1.

How would you write 12^{-3} using only positive exponents?

How would you rewrite \frac{1}{256^{-4}} using only positive exponents?

Select all the expressions that are equivalent to 3^{4}\div 3^{9} = \frac{3^{4}}{3^{9}}

Is 5(\frac{1}{5^{3}})=5(5^{3}) ? Choose the option that best explains the correct answer.

Which of the following is equivalent to 12^{3}\cdot 12^{9}\cdot 12^{4}\cdot 12^{2} ?

Use the laws of exponents to write an equivalent expression that is maximally concise.7q^{2}r^{1}\cdot 4q^{-3}r^{2}

Use the laws of exponents to write an equivalent expression that is maximally concise.\frac{(\frac{1}{2})^{-1}a^{2}b^{-2}c^{5}}{a^{2}b^{-3}c^{2}}

Use the laws of exponents to write an equivalent expression that is maximally concise.(\frac{3m^{2}n^{7}}{m})^{5}

Stephen King is a famously prolific writer, having published over 60 novels and 200 short stories. If King wrote 10^{7} words during a period of 10^{3} days, what was his average rate of composition in \frac{\textrm{words}}{\textrm{day}} ?

Multiply:(2x^{3}+\frac{4}{7}x^{2})(x-14)

Every degree-2 polynomial in one variable can be expressed as ax^{2}+bx^{1}+cx^{0} \textrm{, where } a, b, c \in \mathbb{R} \textrm{ and } a\neq0Create an example where multiplying two, degree 2 polynomials does not yield another degree 2 polynomial.

Use the laws of exponents to write an equivalent expression that is maximally concise.
7q^{2}r^{1}\cdot 4q^{-3}r^{2}

Use the laws of exponents to write an equivalent expression that is maximally concise.
\frac{(\frac{1}{2})^{-1}a^{2}b^{-2}c^{5}}{a^{2}b^{-3}c^{2}}

Use the laws of exponents to write an equivalent expression that is maximally concise.
(\frac{3m^{2}n^{7}}{m})^{5}

Multiply:

(2x^{3}+\frac{4}{7}x^{2})(x-14)

Every degree-2 polynomial in one variable can be expressed as ax^{2}+bx^{1}+cx^{0} \textrm{, where } a, b, c \in \mathbb{R} \textrm{ and } a\neq0

Create an example where multiplying two, degree 2 polynomials does not yield another degree 2 polynomial.