Advertisements
Advertisements
Question
`((-1)/4)^3 xx ((-1)/4)^- = ((-1)/4)^11`
Advertisements
Solution
`((-1)/4)^3 xx ((-1)/4)^bb(underline(8)) = ((-1)/4)^11`
Explanation:
Let `((-1)/4)^3 xx ((-1)/4)^x = ((-1)/4)^11`
⇒ `((-1)/4)^x = ((-1)/4)^11/((-1)/4)^3`
⇒ `((-1)/4)^x = ((-1)/4)^(11 - 3)` ...[∵ am ÷ an = am – n, m > n]
⇒ `((-1)/4)^x = ((-1)/4)^8`
Since, base are equal.
So, by equating the powers, we get
x = 8
∴ `((-1)/4)^3 xx ((-1)/4)^8 = ((-1)/4)^11`
APPEARS IN
RELATED QUESTIONS
Using laws of exponents, simplify and write the answer in exponential form:
`(5^2)^3 ÷ 5^3`
Using laws of exponents, simplify and write the answer in exponential form:
`(2^20 ÷ 2^15) xx 2^3`
Simplify and express the following in exponential form:
((52)3 × 54) ÷ 57
Simplify and express the following in exponential form:
254 ÷ 53
Find the value.
(−7)12 ÷ (−7)12
Simplify:
`(2/3)^6 div (2/3)^9`
For non-zero numbers a and b, `(a/b)^m ÷ (a/b)^n`, where m > n, is equal to ______.
`(-3)^8 ÷ (-3)^5 = (-3)^-`.
`(5/8)^9 ÷ (5/8)^4 = (5/8)^4`
Find the value of:
77 ÷ 77
