Simplification and answer in exponential form of [(2²)³ × 3⁶] × 5⁶ is
Answers
Answer:
MARK AS BRAINLIEST
Step-by-step explanation:
For example:
1. 5³ ×5⁶
= (5 × 5 × 5) × (5 × 5 × 5 × 5 × 5 × 5)
= 53+6, [here the exponents are added]
= 5⁹
2. (-7)10 × (-7)¹²
= [(-7) × (-7) × (-7) × (-7) × (-7) × (-7) × (-7) × (-7) × (-7) × (-7)] × [( -7) × (-7) × (-7) × (-7) × (-7) × (-7) × (-7) × (-7) × (-7) × (-7) × (-7) × (-7)].
= (-7)10+12, [Exponents are added]
= (-7)²²
3. (12)4 × (12)3
=[(12) × (12) × (12) × (12)] × [(12) × (12) × (12)]
=(12)4+3
=(12)⁷
4. 3² × 3⁵
= 32+5
= 3⁷
5. (-2)⁷ × (-2)³
= (-2)7+3
= (-2)10
6. (49)³ × (49)²
= (49)3+2
= (49)⁵
We observe that the two numbers with the same base are
multiplied; the product is obtained by adding the exponent.
2. Dividing Powers with the same Base
For example:
3⁵ ÷ 3¹, 2² ÷ 2¹, 5(²) ÷ 5³
In division if the bases are same then we need to subtract the exponents.
Consider the following:
2⁷ ÷ 2⁴ = 2724
= 2×2×2×2×2×2×22×2×2×2
= 27−4
= 2³
5⁶ ÷ 5² = 5652
= = 5×5×5×5×5×55×5
= 56−2
= 5⁴
10⁵ ÷ 10³ = 105103
= 10×10×10×10×1010×10×10
= 105−3
= 10²
7⁴ ÷ 7⁵ = 7475
= 7×7×7×77×7×7×7×7
= 74−5
= 7−1
Let a be a non zero number, then
a⁵ ÷ a³ = a5a3
= a×a×a×a×aa×a×a
= a5−3
= a²
again, a³ ÷ a⁵ = a3a5
= a×a×aa×a×a×a×a
= a−(5−3)
= a−2
Thus, in general, for any non-zero integer a,
aᵐ ÷ aⁿ = aman = am−n
Note 1:
Where m and n are whole numbers and m > n;
aᵐ ÷ aⁿ = aman = a−(n−m)