Can anyone tell all laws of exponent with verify it with negetive integer pls it's urgent
I will mark as brain lest who gives the first Answer
Answers
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
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)
Answer:
exponent: there is nothing mysterious! an exponent simply shorthand for multiplying that no. of identical factor . so 4 ki power3 is the same as (4) (4) (4), three identical factor of 4. and xki power 3 is just three factors of x, (x) ( x) (x) .
one warning : exponent are the first operation . exponent are the first operation ( in the absence of grouping symbols like parenthese) , so the exponent applies only to what its directly attached to . 3xki power3 is 3( x), (x),( x),not ( 3x) , ( 3x), (3x), if we wanted (3x) (3x) ( 3x) we need to use grouping : (3x) ki power 3
Step-by-step explanation:
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