Let’s solve each problem step by step, without using a calculator. We’ll use the rules of exponents and order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
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1.1
5¹ – 9²
= 5 – 81
=
–76
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1.2
6³ – (–3)⁴ + 3
First, calculate powers:
6³ = 6 × 6 × 6 = 216
(–3)⁴ = (–3) × (–3) × (–3) × (–3) = 81 (even power → positive)
Now plug in:
216 – 81 + 3
= 135 + 3
=
138
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1.3
10² – 2³ – (–2)²
Calculate each term:
10² = 100
2³ = 8
(–2)² = 4
So:
100 – 8 – 4
= 92 – 4
=
88
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1.4
3² × (5⁶ / 5⁴)
Use exponent rule: 5⁶ / 5⁴ = 5^(6-4) = 5²
So:
3² × 5² = 9 × 25 =
225
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1.5
(–5)³ + 4¹ – 5³
Calculate each:
(–5)³ = –125
4¹ = 4
5³ = 125
So:
–125 + 4 – 125
= –121 – 125
=
–246
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1.6
This looks like it might be missing something — probably meant to be “6⁻⁴” or similar? But as written: “6⁴” with a bar over it? That doesn’t make sense mathematically. Let’s assume it’s a typo and should be
6⁻.
If so:
6⁻⁴ = 1 / 6⁴ = 1 / 1296
But since no operation is given, maybe it’s just asking for value? Or perhaps it’s part of another expression? Looking at context, maybe it’s standalone.
Wait — looking again: In original image, 1.6 is written as “6⁴” with a horizontal line above — that could mean negative exponent? Sometimes people write ¯4 to mean -4.
Assuming it’s
6⁻⁴, then answer is
1/1296
But if it’s just 6⁴, then 6×6×6×6 = 1296.
Given the pattern of other problems, likely it’s
6⁻⁴ →
1/1296
We’ll go with that.
→
1/1296
*(Note: If this was meant to be something else, please clarify — but based on common notation, we interpret ¯4 as -4)*
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1.7
(3 – 4)² · 1⁴
First: 3 – 4 = –1
Then: (–1)² = 1
1⁴ = 1
So: 1 × 1 =
1
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Next one (no number labeled, but after 1.7):
10⁴ – (–10)²
10⁴ = 10,000
(–10)² = 100
So: 10,000 – 100 =
9,900
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1.9
(4⁹ · 3²) / 4⁶ – 1²
First, simplify fraction: 4⁹ / 4⁶ = 4^(9-6) = 4³
So: 4³ · 3² – 1
4³ = 64, 3² = 9 → 64 × 9 = 576
Then subtract 1: 576 – 1 =
575
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1.10
(2⁵ · 6¹ · 2²) / 2⁶
Combine numerator: 2⁵ · 2² = 2^(5+2) = 2⁷
So now: (2⁷ · 6) / 2⁶ = 2^(7-6) · 6 = 2¹ · 6 = 2 × 6 =
12
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1.11
Not visible in your text — skipped.
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1.12
10⁴ ÷ 10¹ + (10² × 10³)
First division: 10⁴ ÷ 10¹ = 10^(4-1) = 10³ = 1000
Inside parentheses: 10² × 10³ = 10^(2+3) = 10⁵ = 100,000
Now add: 1000 + 100,000 =
101,000
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Final Answers:
1.1: –76
1.2: 138
1.3: 88
1.4: 225
1.5: –246
1.6: 1/1296 (assuming 6⁻⁴)
1.7: 1
(unnumbered): 9900
1.9: 575
1.10: 12
1.12: 101000
──────────────────────────────────────
Final Answer:
1.1: -76
1.2: 138
1.3: 88
1.4: 225
1.5: -246
1.6: 1/1296
1.7: 1
(unlabeled after 1.7): 9900
1.9: 575
1.10: 12
1.12: 101000
Parent Tip: Review the logic above to help your child master the concept of 8th grade exponents worksheet.
