Given the data from the question, the expressions that are equal to 10⁵ are
- 10³ ⋅ 10²
- 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10
To determine the expressions that are equal to 10⁵, we shall evaluate the options given from the question.
How to evaluate (10⁴)¹
Recall
(Aᵐ)ⁿ = Aᵐⁿ
Thus,
(10⁴)¹ = 10⁴
How toevaluate 10³ ⋅ 10²
Recall
Aᵐ ⋅ Aⁿ = Aᵐ⁺ⁿ
Thus,
10³ ⋅ 10² = 10³⁺²
10³ ⋅ 10² = 10⁵
How to evaluate 1 / 10⁵
Recall
1 / Aᵐ = A⁻ᵐ
Thus,
1 / 10⁵ = 10⁻⁵
How to evaluate (10³)²
Recall
(Aᵐ)ⁿ = Aᵐⁿ
Thus,
(10³)² = 10⁶
How to evaluate 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10
Recall
Aᵐ ⋅ Aⁿ = Aᵐ⁺ⁿ
10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10¹⁺¹⁺¹⁺¹⁺¹
10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10⁵
SUMMARY
(10⁴)¹ = 10⁴
10³ ⋅ 10² = 10⁵
1 / 10⁵ = 10⁻⁵
(10³)² = 10⁶
10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10⁵
From the above illustrations, only 10³ ⋅ 10² and 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 are equal to 10⁵
Complete question
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