Answer: 1. Multiplying Powers with same Base
For example: x² × x³, 2³ × 2⁵, (-3)² × (-3)⁴
In multiplication of exponents if the bases are same then we need to add the exponents.
Consider the following:
1. 2³ × 2² = (2 × 2 × 2) × (2 × 2) = 23+2
= 2⁵
2. 3⁴ × 3² = (3 × 3 × 3 × 3) × (3 × 3) = 34+2
= 3⁶
3. (-3)³ × (-3)⁴ = [(-3) × (-3) × (-3)] × [(-3) × (-3) × (-3) × (-3)]
= (-3)3+4
= (-3)⁷
4. m⁵ × m³ = (m × m × m × m × m) × (m × m × m)
= m5+3
= m⁸
From the above examples, we can generalize that during multiplication when the bases are same then the exponents are added.
aᵐ × aⁿ = am+n
In other words, if ‘a’ is a non-zero integer or a non-zero rational number and m and n are positive integers, then
aᵐ × aⁿ = am+n
Similarly, (ab
)ᵐ × (ab
)ⁿ = (ab
)m+n
(ab)m×(ab)n=(ab)m+n
Note:
(i) Exponents can be added only when the bases are same.
(ii) Exponents cannot be added if the bases are not same like
m⁵ × n⁷, 2³ × 3⁴
Explanation: