Algebra II - Rules for exponents and radical expressions
29
If the radical function is even it means the domain and range is restricted. *(true = 29 or false = 30)*
27
If the radical function is odd it means the domain and range is all real numbers *(true = 27 or false = 28)*
28
If the radical function is odd it means the domain and range is restricted. *(true = 27 or false = 28)*
8
In raising an expression to a power, that power can be applied over multiplication but not division. *(true = 7 or false = 8)*
7
In raising an expression to a power, that power can be applied over multiplication or division. *(true = 7 or false = 8)*
14
Raising a base to a rational exponent with a denominator of n is not the same as taking the nth root of the base. If x is negative, n must be even. If x, is positive, n can be any integer less than or equal to 2. *(true = 13 or false = 14)*
13
Raising a base to a rational exponent with a denominator of n is the same as taking the nth root of the base. If x is negative, n must be odd. If x, is positive, n can be any whole number greater than or equal to 2. *(true = 13 or false = 14)*
33
The square root of a negative radicand will always result in no real number. *(true = 33 or false = 34)*
34
When adding radicals only add the index and keep the radicand the same. *(true = 34 or false = 35)*
35
When adding radicals only add the radicand and keep the index the same. *(true = 34 or false = 35)*
12
When any exponential expression with a base other than zero is raised to the power of zero, the expression will equal 0. *(true =11 or false = 12)*
11
When any exponential expression with a base other than zero is raised to the power of zero, the expression will equal 1. *(true =11 or false = 12)*
4
When dividing exponential expressions that have the same base, add the exponents. *(true = 3 or false = 4)*
3
When dividing exponential expressions that have the same base, subtract the exponents. *(true = 3 or false = 4)*
1
When multiplying exponential expressions that have the same base, add the exponents. *(true =1 or false = 2)*
2
When multiplying exponential expressions that have the same base, subtract the exponents. *(true =1 or false = 2)*
10
When raising a base to a negative exponent, keep the base the same but raise it to the absolute value of the exponent. *(true = 9 or false = 10)*
9
When raising a base to a negative exponent, the reciprocal of that base is raised to the absolute value of the exponent. *(true = 9 or false = 10)*
6
When raising an exponential expression to another power, add the exponents. *(true = 5 or false = 6)*
5
When raising an exponential expression to another power, multiply the exponents. *(true = 5 or false = 6)*
36
When subtracting radicals only add the index and keep the sign of the larger index. Keep the radicand the same. *(true = 36 or false = 37)*
37
When subtracting radicals only add the radicand and keep the sign of the larger radicand. Keep the index the same. *(true = 36 or false = 37)*
15
An index, or power, is used to show that a quantity is repeatedly multiplied by itself. *(true = 15 or false = 16)*
16
An index, or power, is used to show that a quantity is repeatedly multiplied by the radicand. *(true = 15 or false = 16)*
38
Even if there is no coefficient near the index, there is an implied 1. *(true = 38 or false = 39)*
17
The radicand is how many times it needs to be multiplied by the index or power. *(true = 17 or false = 18)*
powers of products rule
*Identify rule for exponent*
powers of quotients rule
*Identify rule for exponent*
product rule
*Identify rule for exponent*
quotient rule
*Identify rule for exponent*
rational rule
*Identify rule for exponent*
zero rule
*Identify rule for exponent*
a^4
(a^-2)^-2
b^-6
(b^3)^-2
negative rule
*Identify rule for exponent*
power rule
*Identify rule for exponent*
21
Regarding the exponent rule pertaining to negative exponents, moving the negative exponent requires the sign to change in any direction (up or down) *(true = 21 or false = 22)*
22
Regarding the exponent rule pertaining to negative exponents, moving the negative exponent requires the sign to change only when moving down *(true = 21 or false = 22)*
24
Regarding the exponent rule pertaining to the power rule, (b^3)^-2 implies that you need to multiply -3 by -3 *(true = 23 or false = 24)*
23
Regarding the exponent rule pertaining to the power rule, (b^3)^-2 implies that you need to multiply 3 by -2 *(true = 23 or false = 24)*
26
Regarding the exponent rule pertaining to the power rule, (b^3)^-2 implies that you need to multiply 3 by 2 *(true = 25 or false = 26)*
19
Regarding the exponent rule, negative exponents becomes part of the denominator and we take the absolute value of that exponent. *(true = 19 or false = 20)*
20
Regarding the exponent rule, negative exponents becomes part of the numerator and we change the sign to positive. *(true = 19 or false = 20)*
32
Simplifying most radicals requires knowledge of perfect squares and cubes only. *(true = 31 or false = 32)*
31
Simplifying most radicals requires prime factorization and knowledge of perfect squares and cubes. *(true = 31 or false = 32)*
40
With regards to multiplying radicals, if you multiply radicals with different indexes, you must find the LCD first. *(true = 40 or false = 41)*
41
With regards to multiplying radicals, you can multiply radicals if they have different indexes. *(true = 40 or false = 41)*
46
With regards to multiplying radicals, you need to multiply the coefficients and the radicands and find the perfect square or cube or prime factorization for the radicand. *(true = 46 or false = 47)*
47
With regards to multiplying radicals, you need to multiply the coefficients with the radicands and only use the perfect square factors when possible*(true = 46 or false = 47)*
55
With regards to radical equations, it is not possible to have a quadratic. *(true = 54 or false = 55)*
54
With regards to radical equations, it is possible to have a quadratic in which the zero product property is necessary to solve for both scenarios of x . *(true = 54 or false = 55)*
52
With regards to radical equations, you need to check your answers if you have two solutions because one of the solutions can be extraneous which is identified as having no solution. *(true = 52 or false = 53)*
53
With regards to radical equations, you need to check your answers if you have two solutions because one of the solutions can be extraneous which is identified as having the correct solution. *(true = 52 or false = 53)*
51
With regards to radical equations, you need to remove the radical by raising each side to the 2nd power for any type of radical. *(true = 50 or false = 51)*
50
With regards to radical equations, you need to remove the radical by raising each side to the index of the radical. *(true = 50 or false = 51)*
48
With regards to rationalizing the denominator, you need to multiply the numerator and denominator by the conjugate *(true = 48 or false = 49)*
49
With regards to rationalizing the denominator, you need to multiply the numerator and denominator by the denominator without changing the sign *(true = 48 or false = 49)*
42
With regards to simplifying radicals with higher powers, if the index is to the 3rd power, you must find pairs of 3. *(true = 42 or false = 43)*
43
With regards to simplifying radicals with higher powers, if the index is to the 3rd power, you must find pairs of 4. *(true = 42 or false = 43)*
44
With regards to simplifying radicals, a pair of prime factors needs to be on the left side of the radical and factors with no pairs are left on the inside. *(true = 44 or false = 45)*
45
With regards to simplifying radicals, a pair of prime factors needs to be outside of the radical and factors with no pairs are on the left of the radical. *(true = 44 or false = 45)*
a^8
a^5/a^-3