Advertisements
Advertisements
प्रश्न
Evaluate:
`(3^4 xx 12^3 xx 36)/(2^5 xx 6^3)`
उत्तर
We have, `(3^4 xx 12^3 xx 36)/(2^5 xx 6^3) = (3^4 xx (2^2 xx 3)^3 xx (2^2 xx 3^2))/(2^5 xx (2 xx 3)^3` ......[∵ 12 = 2 × 2 × 3 and 36 = 2 × 2 × 3 × 3]
= `(3^4 xx 2^6 xx 3^3 xx 2^2 xx 3^2)/(2^5 xx 2^3 xx 3^3)` ......[∵ (a × b)m = am × bm]
= `((3^4 xx 3^2 xx 3^3) xx (2^6 xx 2^2))/((2^5 xx 2^3) xx 3^3)`
= `(3^(4+2+3) xx 2^(6+2))/(2^(5+3) xx 3^3)` ......[∵ am × an = am+n]
= `(3^9 xx 2^8)/(3^3 xx 2^8)` = 39–3 × 28–8 ......`[∵ a^m/a^n = a^(m-n)]`
= 36 × 20 = 36 × 1 ......[∵ a0 = 1]
= 729
APPEARS IN
संबंधित प्रश्न
Simplify and express the following in exponential form:
`(a^5/a^3)xx a^8`
Simplify and express the following in exponential form:
`(4^5 xx a^8b^3)/(4^5 xx a^5b^2)`
Simplify:
`((2^5)^2 xx 7^3)/(8^3 xx 7)`
Simplify:
`(3^5 xx 10^5 xx 25)/(5^7 xx 6^5)`
Simplify and express the following in exponential form:
`[(3/7)^4 xx (3/7)^5] ÷ (3/7)^7`
Simplify and express the following in exponential form:
(515 ÷ 510) × 55
Evaluate:
`(7^8 xx a^10b^7c^12)/(7^6 xx a^8b^4c^12)`
Evaluate:
`(125 xx 5^2 xx a^7)/(10^3 xx a^4)`
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)`
