Math Rules

Question 1

If you ADD OR SUBTRACT exponent terms with the same base, then you….

2^3 + 2^5

Answer 1

Pull out the common factor

2^3 (1+2^2)

Question 2

If you ADD OR SUBTRACT exponent terms with different bases, then you…

2^3 + 6^3

Answer 2

Break down the bases and THEN pull out the common factor

2^3 + (2^3x3^3) –> 2^3(1+3^3)

Question 3

If you SQUARE a SQUARE ROOT you get…

Answer 3

The original number being squared/rooted

Question 4

If you square root a square, you get…

Answer 4

The positive value of the original number

Question 5

Square Root of a number X (where X is greater than 1) will be BIGGER OR SMALLER than X?

Answer 5

Smaller

Question 6

Square root of a number X where X is between 0 and 1 will be BIGGER or SMALLER than X?

Answer 6

Bigger

Question 7

If you take the square root of 1 or 0, you get….

Answer 7

The number you started with (1 or 0)

Question 8

A square root is equivalent to an exponent of….

Answer 8

1/2, for exponents with positive bases

Question 9

To take the square root of a positive number that is raised to a power, you…

Root (5^12)

Answer 9

Rewrite the square as an exponent of 1/2, then multiply the exponents

(5^12)^1/2 = 5^6

Question 10

Square root of a negative number?

Answer 10

Is in an imaginary number - can’t take the square root

Question 11

Cube root of a negative number is….

Answer 11

A negative number

Question 12

A cube root is equivalent to an exponent of …

Answer 12

1/3

Question 13

Dealing with fractional exponents. You:

8^2/3

Answer 13

Apply two exponents: the numerator as a power and the denominator as a fractional root, in whatever order seems easiest

(8^2)^1/3 –> Cube root 64 –> 4

Question 14

To multiply or divide square roots, you…

Answer 14

Put everything under the root and then simplify

Question 15

Further simplify a square root that is not a perfect square by…

Root 12

Answer 15

Factoring out squares.

Root 12 can be simplified further:

12 = 4 x 3, and 4 is a perfect square

Root 12 = Root (4x3) = Root 4 x Root 3

2 root 3 = Root 12

Question 16

If you need to simplify a square root and you don’t spot a perfect square…

Root 360

Answer 16

Break the number down into its prime factorization (will take longer but works):

360 –> 2 x 2 x 2 x 3 x 3 x 5

Root 360 = 2x3 Root (2x5) = 6 Root 10

Question 17

To add or subtract under the root, you…

Root (3^2 + 4^2)

Answer 17

Crunch the numbers, if they’re small, OR Pull out common square factors

YOU CANNOT BREAK THIS INTO ROOT 3^2 + ROOT 4^2 –> CAN ONLY DO THAT WITH MULTIPLICATION

Root (4^14 + 4^16) =

Question 18

If you MULTIPLY exponential terms with the same base… then you

X^2 x x^3

Answer 18

Add the exponents

X^2 x X^3 = X ^ 5

Question 19

If you DIVIDE exponential terms with the same base, then you . . .

(A^5)
______
(A ^3)

Answer 19

Subtract the exponents

A ^ 5
______
A ^ 3

=

A^2

Question 20

Raise anything to the power of zero, besides zero itself, you get a ….

Answer 20

1

Question 21

Raise a zero to a negative power, you get a ….

Answer 21

Impossible number

Question 22

Raise anything else to a negative power, get a

A ^ -2

Answer 22

1 over the same number to a corresponding positive power

A ^ -2 = 1 / a^2

Question 23

To move a term from the numerator or denominator of a fraction, you…

(2a^-2)/3 =

Answer 23

Switch the positive or negative sign

(2a^-2)/3 = 2/3a^2

Question 24

If you raise something to two successive powers…

(A^2)^4

Answer 24

Multiply the powers

(a^2)^4 = a^8

Question 25

To apply an exponent to a product

(ab)^3

Answer 25

Apply the exponent to each factor of the product

Ab)^3 = (a^3)(b^3

Question 26

To apply an exponent to an entire fraction…

(a/b)^4

Answer 26

Apply the exponent separately to the top and the bottom

(a/b)^4 = a^4/b^4

Question 27

If you see two factors with the same exponent, you might…

a^3 x b^3

Answer 27

Regroup the factors as a product

a^3 x b^3 = (ab)^3

Question 28

To add or subtract terms with the same base, you…

2^3 + 2^5

Answer 28

Pull out the common factor

2^3 + 2^5 –> 2^3 (1+2^2)

Question 29

To add or subtract terms with different bases…

2^3 + 6^3

Answer 29

Break down the bases and pull out the common factor

2^3 + 6^3 –> 2^3 + (2^3x3^3) –> 2^3(1+3^3)