options: Extend the properties of exponents to rational exponents.

Use properties of rational and irrational numbers.

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

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

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

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

Perform operations on vectors.

Reason quantitatively and use units to solve problems.

Represent and model with vector quantities.

Use complex numbers in polynomial identities and equations.

Represent complex numbers and their operations on the complex plane.

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

Perform arithmetic operations with complex numbers.

Perform operations on matrices and use matrices in applications.
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: 1