Exponents

Question 1

When can I add or subtract exponents?

Answer 1

When the bases are the SAME

EX.
(10^4)*(10^3) = 10^7

The base is 10.
(Multiplication = ADD)
(Division = SUBTRACT)

Reverse this rule…how to factor 3 ^ ( a + 1 )?

3^a * 3^1

Anytime I see an exponent with an + or - sign, then use the same base and either X or Divide to factor it out.

Question 2

Any number ^ 0 =

Answer 2

1

Question 3

0 ^ Any number =

Answer 3

0 (Think about it…000*0 etc…)

Question 4

When raising a fraction/decimal between (0 and 1) to an exponent, the value gets…?

Answer 4

Smaller

EX.
.75)(.75)(.75

Question 5

-2^2 = 4?

Answer 5

NO
It equals (-4)

4 would be the answer to this question
(-2)^2

It must be in the parenthesis.

Question 6

Is this valid? (3/4)^1 = (3^1)/(4^1)

Answer 6

Yes

Question 7

Is this valid? (12)^3 = (3*4)^3

Answer 7

Yes

Question 8

When you raise an exponential term to an exponent, what operation should be used?

EX.

(4^3)^3

Answer 8

Multiplication

4^9

Question 9

How can this expression be rewritten?

3^(4/3)

Answer 9

This equals the cubed root of 3^4.

The numerator is the power.
The denominator is the root.

Question 10

How to factor and exponential expression.
EX.
3^10+3^8+3^4 = ?

Answer 10

(3^4)((3^6)+(3^4)+(1))

Question 11

When a problem involves exponential expressions on both sides of the equation, it is imperative to rewrite the equation with the same bases or with the same exponents. Once the bases or exponents are the same, eliminate them and solve for the remainder of the problem.

Answer 11

EX - pg. 43 - Algebra

Question 12

Fractions side by side, perform which operation?
45 4
_ X _
1 15

Answer 12

Multiplication

= 180/15

Question 13

Is this valid? 4(3^3) = (12)^3

Answer 13

No!
This is in it’s simplest form.

When could you multiply the 4 into the (expression)?

If 4 had an exponent of 3 also.
(4^3)*(3^3) = (12)^3

Question 14

Is this valid? (2^10) + (2^10) + (2^10) = 2^30

Answer 14

No!

It equals 4(2^10)

Question 15

Factor Exponents…

How does this work [4(4y0] = (4^(y+1))

Answer 15

?

Question 16

(333)^2 can also be written as ?

Answer 16

(3^3)^2 = 3^6

Question 17

When you see What is the value of (8^3)(32^2)(16^-4) how do you solve?

Answer 17

Break down each into factors. Re-write exponents. Add exponents.

Question 18

If both sides of an equation have exponential expressions, how can you solve?

Answer 18

Make the bases the same. Once that is complete, you can drop the basis and solve the exponents as the new equation.

Question 19

When there are exponents in the problem, look to?

Answer 19

make the numbers have the same base

Question 20

If exponential terms are being added, you have to?

Answer 20

solve for each term before adding (If the exponents are large, then there is usually some trick to simplify the exponents before solving.)