Exponents & Scientific Notation — Drills
Exponents & Scientific Notation has 9 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 5 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Base — The number being multiplied. In 53 the base is 5.
- Exponent — How many times the base is used as a factor. In 53 the exponent is 3.
- Power — The whole expression, 53, and also its value, 125.
- Scientific notation — A number written as a × 10n, where 1 ≤ a < 10.
- Standard form — The ordinary way of writing a number, like 47,000.
Evaluating
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Evaluate 63.
Worked answer
216
6 × 6 × 6 = 216
Problem 2
Evaluate 83.
Worked answer
512
8 × 8 × 8 = 512
Zero
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Evaluate 140.
Worked answer
1
Follow the pattern down: 142, 141 = 14, then 140 = 1.
Problem 2
Evaluate 30.
Worked answer
1
Follow the pattern down: 32, 31 = 3, then 30 = 1.
Product
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Simplify 63 · 62 and give its value.
Worked answer
7776
63+2 = 65
= 7776
Problem 2
Simplify 23 · 24 and give its value.
Worked answer
128
23+4 = 27
= 128
Quotient
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Simplify 4642 and give its value.
Worked answer
256
46-2 = 44
= 256
Problem 2
Simplify 5452 and give its value.
Worked answer
25
54-2 = 52
= 25
Powers
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Simplify (33)3 and give its value.
Worked answer
19683
33 × 3 = 39
= 19683
Problem 2
Simplify (43)2 and give its value.
Worked answer
4096
43 × 2 = 46
= 4096
Negatives
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Evaluate 4-2.
Worked answer
1/16
4-2 = 142
= 116
Problem 2
Evaluate 5-2.
Worked answer
1/25
5-2 = 152
= 125
Scientific
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write 85,000 in scientific notation. Enter just the exponent of 10.
Worked answer
4
Put one non-zero digit in front: 8.5
The point moves 4 places
8.5 × 104
Problem 2
Write 0.00016 in scientific notation. Enter just the exponent of 10.
Worked answer
-4
Put one non-zero digit in front: 1.6
The point moves 4 places
1.6 × 10-4
Scicalc
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Compute (4 × 103)(3 × 102) in scientific notation. Enter just the exponent of 10.
Worked answer
6
4 × 3 = 12
103 · 102 = 105
12 × 105 = 1.2 × 106
Problem 2
Compute (2 × 105)(3 × 101) in scientific notation. Enter just the exponent of 10.
Worked answer
6
2 × 3 = 6
105 · 101 = 106
6 × 106
Comparing
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which is larger, 48 or 74?
- 48
- They are equal
- 74
Worked answer
48
48 = 65536
74 = 2401
65536 > 2401
Problem 2
Which is larger, 27 or 114?
- 27
- 114
- They are equal
Worked answer
114
27 = 128
114 = 14641
14641 > 128