Exponents & Roots

Question 1

What must be true for addition and subtraction of exponents?

Answer 1

They must have the same base and exponent.

I.e. 2r^3 + 6r^3 is okay

You cannot do

2r^5 + 2r^7

Or

4z^7 - 4d^2

Question 2

What must be true in order to multiply exponents?

Answer 2

The numbers must have the same base or exponent

Question 3

How do you multiply exponents?

Answer 3

if they have the same base, you add their exponents and multiply their coefficients

I.e. 4x^2 * 9x^5=36x^7

If they do not have the same base do not add their exponents but do multiply their coefficients

If the term has the same base and exponents you can add their exponents OR multiply their bases

Question 4

How do you multiply an exponent with the same base and same exponent?

Give an example of a problem

Answer 4

You can either add their exponents OR multiply their bases

I.e. 5^x * 5^x = 25x or 5^2x

Question 5

How do you multiply exponential terms with the same base ?

Give an example.

Answer 5

You add their exponents and multiply their coefficients

I.e. 3z^2 x 4z^3= 12z^5

Question 6

How do you multiply an exponential term with the same exponent?

Give an example.

Answer 6

You multiply their bases and multiply their coefficients

I.e. 7d^4 * 5d^4= 35d^4

Question 7

How do you divide a term with an exponent if it has the same base?

What do you do if it has a coefficient?

Give An example

Answer 7

You subtract their exponents

Do not divide their bases but do divide their coefficients

z^7 / z^5 = z^2

Question 8

How do you divide a term that has the same exponent?

What if it has a coefficient?

Give an example.

Answer 8

Divide their bases and divide their coefficients

I.e. 9^4 / 3^4= 3^4

Question 9

What is the answer to a division equation where there is a term with an exponent with the same base and exponent?

Answer 9

The quotient if their coefficients times 1

I.e. 5^3 / 5^3= 1
8x^4 / 4x^4=2

Question 10

What do you do with negative exponents?

What if they have a coefficient?

Answer 10

Flip the base and make the exponent positive

Leave the coefficients as they are

Question 11

Does the exponent apply to the base and coefficient of a term?

Answer 11

No, only the base

Question 12

How do you apply fractional roots?

Answer 12

Take the base to the root of the denominator

Then

Use the numerator as the power of the new base

Question 13

How do you solve problems w exponential expressions on both sides of an equations

Answer 13

Make sure that both expressions have the same base or same exponent

Eliminate what is the same

Solve for what is left behind

Question 14

What can be a key to solving some exponent problems that involve addition and subtraction?

Answer 14

Rewrite the problem by reversing the rule

Question 15

How do you handle numbers w large exponents or large bases?

Answer 15

You split the exponent or base

Split exponents by having two exponents that add to the current exponent

Split bases by having bases that multiply to the current base

(Most often the bases will need to be broken down)

Question 16

What should you do if given an exponential expression with a fractional base?

Answer 16

Rewrite the base

Question 17

An even number times any number results in a ___solution?

Answer 17

Even

Question 18

All powers of 6 are….?

Answer 18

Even

Question 19

What is the opposite of a root?

Answer 19

An exponent

Question 20

A negative root is denoted by what?

Answer 20

A negative radical

Question 21

What is the square root rule for square 2-10

Answer 21

From sq root of 4 it increases by .2

From sq root of 4 it decreases by .3

Question 22

How do you simplify a sq root ?

Answer 22

Rewrite the root as a product of its factors inside the radical and simplify any pairs that lie within

Question 23

When cant a sq root be simplified?

Answer 23

When it does not contain a pair of factors

Question 24

What should you remember when a root has a coefficient and you are factoring the root?

Answer 24

Multiply the coefficient w the pair you put outside the radical

Question 25

How do you simplify a simple square root (roots w/o addition or subtraction)

Answer 25

Break up the root

Question 26

How do you simplify complex roots (roots w addition or subtraction)

Answer 26

combine terms within the radical

Question 27

What roots can be added or subtracted?

Answer 27

Those w the same radical

Question 28

How do you multiply square roots?

Answer 28

Combine terms under a single radical (simplify terms to make things easier)

Multiply coefficients together if you have them

Question 29

How do you divide square roots?

Answer 29

Break down radicals and cancel out like terms

Be sure to keep coefficients separate

Question 30

Whats the best way to approximate a square root?

Answer 30

Think of squares that the number lies between

Question 31

How do you get a root out of the denominator in a non complex denominator?

Answer 31

Multiply the top and bottom of the fraction by that root

Question 32

How do you simplify a complex radical denominator?

Answer 32

Multiply the equation by the conjugate of the denominator

Question 33

What is key to solving complex square root problems?

Answer 33

Factoring out terms in common within the denominator and looking for common perfect squares once u simplify the terms

Question 34

Decimal places of answer x root number = decimal places of original

Answer 34

How to calculate roots And decimals

Question 35

Whats the easiest way to multiply square roots?

Answer 35

Combine the terms under a single radical

Question 36

What numbers have square roots, cube roots, and quarter roots that are less than 1

Answer 36

Only numbers less than 1

Question 37

What is 2^29 - 2^28 =

Answer 37

2^28(2-1)= 2^28

Question 38

How do you solve 101^2 - 99^2 ?

Answer 38

Do difference of squares

(101+99)(101-99)=200(2)=400

Question 39

If a root has a coefficient it is better to convert the coefficient to a root. Provide an example.

Answer 39

If you have 3 sq rt 7

Turn the 3 into a sq rt of 9

Multiply sq rt 9 by sq rt 7 and gget sq rt 63

Sq rt 63 is a bit less than sq rt 64 which is 8

So sq rt 63 is approx. 7.9