options: Reason quantitatively and use units to solve problems.

Perform arithmetic operations with complex numbers.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Represent and model with vector quantities.

Compute fluently with multi-digit numbers and find common factors and multiples.

Perform operations on matrices and use matrices in applications.

Use properties of rational and irrational numbers.

Use complex numbers in polynomial identities and equations.

Represent complex numbers and their operations on the complex plane.

Perform operations on vectors.

Apply and extend previous understandings of numbers to the system of rational numbers.

Extend the properties of exponents to rational exponents.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Know that there are numbers that are not rational, and approximate them by rational numbers.
problem_activity: Provide a written explanation for each question below.
a.   Is it true that
$${\left(1000^{1\over3}\right)^3=(1000^3)^{1\over3}}$$
? Explain or show how you know.
b.   Is it true that
$${\left(4^{1\over2}\right)^3=(4^3)^{1\over2}}$$
? Explain or show how you know.
c.   Suppose that
$$m$$
and
$$n$$
are positive integers and
$$b$$
is a real number so that the principal
$$n^{th}$$
root of
$$b$$
exists. In general, does
$$\left(b^{1\over n}\right)^m=(b^m)^{1\over n}$$
? Explain or show how you know.


correct_option_index: 6