Evidence of Understanding

**compare and contrast exponential functions with other functions that contain exponents**- describe similarities and differences between
**power**and**exponential**models- compare graphs of power functions and exponential functions (focus on y = x
^{2}and y = 2^{x}, y = x^{3}and y = 3^{x}, and y =*√*x and y = ½^{x}) *possible extension: notice similarities between x*^{2}and 2^{x}and use that to anticipate and describe possible similarities between √x and the inverse of 2^{x}

- compare graphs of power functions and exponential functions (focus on y = x
- generate and justify a function rule from a table, sequence, graph, or situation
- determine when a power, exponential, or neither function model is appropriate

- determine when a power, exponential, or neither function model is appropriate

- describe similarities and differences between
**investigate and transform expressions containing exponents into equivalent forms**- rewrite expressions using exponent properties
*a*^{m}*● a*^{n}*= a*^{m + n}(product),*(a*^{m}*)*^{n}*= a*^{mn}(power),*a*^{0}**= 1**(zero),*a*^{m}*/a*^{n}*= a*^{m - n}^{}(quotient), and*a*^{-m}*= 1/a*^{m}- explore and describe the
**commutativity**of exponent rules - prove expressions with different
**bases**are equivalent*(Example: 64*^{3}*= 8*^{6}*= 4*^{9}*= 2*^{18}*)*

- explore and describe the
- explain the relationship between a
**rational exponent**and its equivalent**radical**form- connect the definition of a
**square root**or**cube root**to its equivalent exponent

- connect the definition of a
- convert between expressions with radicals and expressions with rational exponents

- rewrite expressions using exponent properties
**analyze and evaluate expressions or equations using properties of exponents**- identify equations or expressions that can be rewritten with common bases to solve problems
*Example: solve 3*^{2x}*= 27*^{x + 1}*by rewriting as 3*^{2x}*= (3*^{3}*)*^{x + 1}^{}or solve (*1**/**16**)*^{x}^{}+ 13 = 77 by simplifying and rewriting as (2^{-4}*)*^{x}*= 2*^{6}

- evaluate expressions and solve equations using radicals or rational exponents
*Example: Evaluate 81*^{3/2}*or**7**√**(128*^{4}*) or Solve (5x - 2)*^{5/3}*- 1 = 31*- apply properties of exponents and common bases to evaluate
__without a calculator__ - use rational exponents to determine an unknown base rate

- identify equations or expressions that can be rewritten with common bases to solve problems

Develop conceptual understanding:

power function, exponential function, exponent properties, commutative, base, exponent, rational exponent, radical form, square root, cube root

Supporting terms to communicate:

function, dependent, independent, input, output, domain, range, integer, rational number, equation, expression