Exploring Exponents

2-26-07

Know the parts of exponential expressions:

What are exponents for/what do they tell us?

1. What is another way to write, using exponents?

2. Write out as repeated multiplication.

3. Write out as repeated multiplication, then simplify it using exponents.

4. Write out as repeated multiplication, then simplify it using exponents.

Can you generalize? What is the shortcut for multiplying exponent expressions with the same base?

Rule:

5. Using this rule, rewrite the following as a single term with exponents:

a) = b) =

c) = d) =

e) = f) =

6. Does this pattern work for different bases? Ex: Why?

7. What does mean?

8. Write out using repeated multiplication, then simplify it again using exponents.

9. Write out using repeated multiplication, then simplify it again using exponents.

Can you generalize? What is the shortcut for raising an exponential expression to another exponent? (power to a power)?

Rule:

5. Using this rule (and perhaps the first one too!), rewrite the following as a single term with exponents:

a) = b) =

c) = d) =

e) = f) =

What does mean?

Write out as repeated multiplication then simplify it using exponents.

Writeout as repeated multiplication then simplify it using exponents.

Write out as repeated multiplication then simplify it using exponents.

Can you generalize? What is the shortcut for raising the product to an exponent? (Product to a power)?

Rule:

5. Using this rule (and perhaps the first ones too!), rewrite the following as a single term with exponents:

a) = b) =

c) = d) =

e) = f) =

Exponent Exploration Part 2

03-01-07

1) Rewrite as repeated multiplication. Reduce the numbers.

2) Using the factors that are left, write them back in a form involving exponents.

3) Rewrite as repeated multiplication, REDUCE and REWRITE the remaining factors with exponents.

Can you generalize? What is the shortcut for taking the quotient of exponential expressions with the same base?

Rule:

4) Simplify the following exponential expressions

a) = b) =

c) = d) =

e) = f) =

5) Does this pattern work if the bases are different? For instance: Why?

6) Rewrite using repeated multiplication, then simplify it again using exponents.

7) Rewrite using repeated multiplication, then simplify it again using exponents.

Can you generalize? What is the shortcut for taking the quotient of exponential expressions with the same base?

Rule:

8) Simplify the following exponential expressions

a) b)

c) d)

e) f)

Simplifying Exponents Part 3

03-02-07

1) Rewrite using repeated multiplication, then reduce the factors.

1 a) Use the shortcut for dividing exponential expressions with the same base to simplify this in terms of powers of x.

2) Rewrite using repeated multiplication, then reduce the factors

2 a) Use the shortcut for dividing exponential expressions with the same base to simplify this in terms of powers of 3

Can you generalize? What is the shortcut for raising an expression to the zero power?

Rule:

3) Rewrite using repeated multiplication, then reduce the factors, simplifying what remains

3 a) Use the shortcut for dividing exponential expression with the same base to simplify this in terms of powers of x

4) Rewrite using repeated multiplication, then reduce the factors simplifying what remains

4 a) Use the shortcut for dividing exponential expressions with the same base to simplify this in terms of powers of x

Can you generalize? What is the shortcut for raising an expression to a negative power?

Rule: