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Flashcards in Exponents & Roots Deck (39)
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1
Q

What must be true for addition and subtraction of exponents?

A

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

2
Q

What must be true in order to multiply exponents?

A

The numbers must have the same base or exponent

3
Q

How do you multiply exponents?

A

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

4
Q

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

Give an example of a problem

A

You can either add their exponents OR multiply their bases

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

5
Q

How do you multiply exponential terms with the same base ?

Give an example.

A

You add their exponents and multiply their coefficients

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

6
Q

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

Give an example.

A

You multiply their bases and multiply their coefficients

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

7
Q

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

A

You subtract their exponents

Do not divide their bases but do divide their coefficients

z^7 / z^5 = z^2

8
Q

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

What if it has a coefficient?

Give an example.

A

Divide their bases and divide their coefficients

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

9
Q

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

A

The quotient if their coefficients times 1

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

10
Q

What do you do with negative exponents?

What if they have a coefficient?

A

Flip the base and make the exponent positive

Leave the coefficients as they are

11
Q

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

A

No, only the base

12
Q

How do you apply fractional roots?

A

Take the base to the root of the denominator

Then

Use the numerator as the power of the new base

13
Q

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

A

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

Eliminate what is the same

Solve for what is left behind

14
Q

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

A

Rewrite the problem by reversing the rule

15
Q

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

A

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)

16
Q

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

A

Rewrite the base

17
Q

An even number times any number results in a ___solution?

A

Even

18
Q

All powers of 6 are….?

A

Even

19
Q

What is the opposite of a root?

A

An exponent

20
Q

A negative root is denoted by what?

A

A negative radical

21
Q

What is the square root rule for square 2-10

A

From sq root of 4 it increases by .2

From sq root of 4 it decreases by .3

22
Q

How do you simplify a sq root ?

A

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

23
Q

When cant a sq root be simplified?

A

When it does not contain a pair of factors

24
Q

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

A

Multiply the coefficient w the pair you put outside the radical

25
Q

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

A

Break up the root

26
Q

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

A

combine terms within the radical

27
Q

What roots can be added or subtracted?

A

Those w the same radical

28
Q

How do you multiply square roots?

A

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

Multiply coefficients together if you have them

29
Q

How do you divide square roots?

A

Break down radicals and cancel out like terms

Be sure to keep coefficients separate

30
Q

Whats the best way to approximate a square root?

A

Think of squares that the number lies between

31
Q

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

A

Multiply the top and bottom of the fraction by that root

32
Q

How do you simplify a complex radical denominator?

A

Multiply the equation by the conjugate of the denominator

33
Q

What is key to solving complex square root problems?

A

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

34
Q

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

A

How to calculate roots And decimals

35
Q

Whats the easiest way to multiply square roots?

A

Combine the terms under a single radical

36
Q

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

A

Only numbers less than 1

37
Q

What is 2^29 - 2^28 =

A

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

38
Q

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

A

Do difference of squares

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

39
Q

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

A

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