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

Extend the properties of exponents to rational exponents.

Know that there are numbers that are not rational, and approximate them by rational numbers.

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

Represent complex numbers and their operations on the complex plane.

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

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

Represent and model with vector quantities.

Use properties of rational and irrational numbers.

Perform arithmetic operations with complex numbers.

Reason quantitatively and use units to solve problems.

Perform operations on matrices and use matrices in applications.

Perform operations on vectors.

Use complex numbers in polynomial identities and equations.
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: 8