General Exponents
What's the base in this exponential expression:
24
The base is 2
Can the product rule apply to the following problem?
58 * 68
NO!
The product rule can only apply if the bases are the same, and in this problem the bases are 5 and 6.
Can the quotient rule apply to the following problem?
49 ÷ 43
Yes!
Both parts of the problem have the same base (4), so the quotient rule can apply!
Can the power rule apply here?
(82)9
Yes!
All you need to apply the power rule is exponential expression raised to another power.
What is the power in this exponential expression?
412
The power is 12
Rewrite this problem as a single expression using the product rule:
26 * 24
2(6+4) = 210
Can the quotient rule apply to the following problem?
138904 ÷ 138913
No!
The quotient rule can only apply when the bases are the same, and although 13890 and 13891 are very close, they are not the same.
Rewrite this expression using only one power.
(154)3
15(4 * 3) = 1512
Rewrite this exponential expression using repeated multiplication:
85
8 * 8 * 8 * 8 * 8
Rewrite this problem as a single expression using the product rule:
83 * 62
Trick Question! You cannot use the product rule here because the two factors have different bases!
Rewrite this problem as a single expression using the quotient rule:
108 ÷ 103
10(8-3) = 105
Rewrite 612 as an expression with one base and two different powers (Multiple different correct answers!)
(63)4
(62)6
(612)1
Evaluate this exponential expression:
33
27
Rewrite this problem as a single expression using the product rule:
74 * 79 * 72
7(4+9+2) = 715
Rewrite this problem as a single expression using the quotient rule:
49 ÷ 4
4 = 41
4(9-1) = 48
Rewrite this expression using only one power.
((93)2)4
9(3 * 2 * 4) = 924
Evaluate this exponential expression:
15260
1
Solve this problem using the product rule (be sure to show your work):
23 * 22 = ?
25 = 32
Solve this problem using the quotient rule (be sure to show your work):
37 ÷ 35 = ?
32 = 9
Solve this problem using the power rule (be sure to show your work):
(22)2
2(2 * 2) = 24 = 16