Advertisements
Advertisements
Question
Evaluate:
`(125 xx 5^2 xx a^7)/(10^3 xx a^4)`
Advertisements
Solution
We have, `(125 xx 5^2 xx a^7)/(10^3 xx a^4) = (5^3 xx 5^2 xx a^7)/((2 xx 5)^3 xx a^4)` ...[∵ 125 = 53]
= `(5^(3 + 2) xx a^7)/(2^3 xx 5^3 xx a^4)` ...[∵ am × an = am + n and (a × b)m = am × bm]
= `(5^5 xx a^7)/(2^3 xx 5^3 xx a^4)`
= `(5^5/5^3) xx (a^7/a^4) xx (1/2^3)`
= `(5^(5 - 3) xx a^(7 - 4))/2^3` ...`[∵ a^m/a^n = a^(m - n)]`
= `(5^2 xx a^3)/2^3`
= `(25a^3)/8`
APPEARS IN
RELATED QUESTIONS
Simplify and express the following in exponential form:
`(a^5/a^3)xx a^8`
Simplify:
`(25 xx 5^2 xx t^8)/(10^3 xx t^4)`
Simplify:
`(3^5 xx 10^5 xx 25)/(5^7 xx 6^5)`
Simplify and write the answer in the exponential form.
[(22)3 x 36] x 56
Simplify: `(12^4 xx 9^3 xx 4)/(6^3 xx 8^2 xx 27)`
Simplify: `(2 xx 3^4 xx 2^5)/(9 xx 4^2)`
[(–3)2]3 is equal to ______.
Simplify and express the following in exponential form:
`[(7/11)^5 ÷ (7/11)^2] xx (7/11)^2`
Evaluate:
`((6 xx 10)/(2^2 xx 5^3))^2 xx 25/27`
Evaluate:
`(15^4 xx 18^3)/(3^3 xx 5^2 xx 12^2)`
