simplify using the law of exponents.(-4)⁵ × ( -4 ) -¹⁰
Answers
(i) 32 × 34 × 38
Answer
We know that by the rule of multiplying the powers with the same base = am × an = am + n
So the given expression becomes,
= (3)2 + 4 + 8
= 314
(ii) 615 ÷ 610
Answer
We know that by the rule of dividing the powers with the same base = am ÷ an = am – n
So the given expression becomes,
= (6)15 – 10
= 65
(iii) a3 × a2
Answer
We know that by the rule of multiplying the powers with the same base = am × an = am + n
So the given expression becomes,
= (a)3 + 2
= a5
(iv) 7x × 72
Answer
We know that by the rule of multiplying the powers with the same base = am × an = am + n
So the given expression becomes,
= (7)x + 2
(v) (52)3 ÷ 53
Answer
We know that by the rule of taking the power of as power = (am)n = amn
(52)3 can be written as = (5)2 × 3
= 56
Now, 56 ÷ 53
We know that by the rule of dividing the powers with the same base = am ÷ an = am – n
So the given expression becomes,
= (5)6 – 3
= 53
(vi) 25 × 55
Answer
We know that by the rule of multiplying the powers with the same exponents = am × bm = abm
So the given expression becomes,
= (2 × 5)5
= 105
(vii) a4 × b4
Answer
We know that by the rule of multiplying the powers with the same exponents = am × bm = abm
So the given expression becomes,
= (a × b)4
= ab4
(viii) (34)3
Answer
We know that by the rule of taking the power of as power = (am)n = amn
(34)3 can be written as = (3)4 × 3
= 312
(ix) (220 ÷ 215) × 23
Answer
We know that by the rule of dividing the powers with the same base = am ÷ an = am – n
(220 ÷ 215) can be simplified as
= (2)20 – 15
= 25
So the given expression becomes,
We know that by the rule of multiplying the powers with the same base = am × an = am + n
25 × 23 can be simplified as,
= (2)5 + 3
= 28
(x) 8t ÷ 82
Answer
We know that by the rule of dividing the powers with the same base = am ÷ an = am – n
So the given expression becomes,
= (8)t – 2