Exponents and Roots

Question 1

0^0

Answer 1

Undefined
B/c could be 1 * 0 zero times so your left with 1.

OR

Could be zero

Question 2

a^n

Answer 2

means one times n a’s.

Where n is a non-negative number

Question 3

Negative number to an even exponent

Answer 3

Positive

Question 4

Negative number to an odd exponent

Answer 4

Negative

Question 5

Exponents of decimals

Answer 5

Remember that the final answer’s number of decimals (past the decimal point) is the sum of all decimal places of the elements being multiplied.

Question 6

Principal Root

Answer 6

Positive Square root only

Else: +- symbol in front of sqrt

Question 7

x ² = 9

Answer 7

x = 3, x = -3

Question 8

What does it mean to simplify a square root?

Answer 8

It means find the perfect squares to remove from under the square root sign.

Question 9

sqrt(1 / 200)

Answer 9

= sqrt(1) / sqrt(200)

= 1 / 10sqrt(2)

Question 10

a^-x

Answer 10

= 1/a^x

Question 11

(a/b)^-x

Answer 11

(b/a)^x

Question 12

(1/2)^-2

Answer 12

2^2 = 4

Question 13

(2/4)^-2

Answer 13

(4/2)^2

(16/4) = 4

Question 14

Adding and subtracting radicals

Answer 14

Must have like radicands
(Expression under the root)

Only operate on the numbers in front of the radicals

Question 15

Multiply radicals

Answer 15

Must have same index number

3root(x) * 3root(y) = 3root(xy)

Same law as multiplying polynomials:
In general, when multiplying two polynomials together, use the distributive property, until every term of one polynomial is multiplied times every term of the other polynomial. Make sure that you simplify your answer by combining any like terms.

Question 16

Divide radicals

Answer 16

A Quotient of Two Radicals
With the Same Index Number
If n is even, x and y represent any nonnegative real number
and y does not equal 0.

If n is odd, x and y represent any real number and y does not equal 0.

nroot(x) / nsqrt(y) = nroot(x / y)

Question 17

Roots of variables with exponents

Answer 17

Divide exponents by index and sum for new variable exponent combo left of radical.

Remainder goes back under the radical as the exponent of the radicand

eg:
Sqrt(z^7) = z^3 sqrt(z)

Question 18

Raising an exponent to a power

Answer 18

Multiply the exponents, keep base!

** Must have the same base and same index!!

(Z^3)^2 x Z = Z^7

2^2 x 2^3 = 2^5 = 32

Question 19

Multiplying exponents

Answer 19

Add exponents, keep base!

**Must have the same base and same index!!

(Z^3)^2 x Z = Z^7

2^2 x 2^3 = 2^5 = 32