Advertisements
Advertisements
Question
Evaluate:
`(15^4 xx 18^3)/(3^3 xx 5^2 xx 12^2)`
Advertisements
Solution
We have, `(15^4 xx 18^3)/(3^3 xx 5^2 xx 12^2) = ((3 xx 5)^4 xx (2 xx 3^2)^3)/(3^3 xx 5^2 xx (2^2 xx 3)^2)` ...[∵ 18 = 2 × 3 × 3 and 12 = 2 × 2 × 3]
= `(3^4 xx 5^4 xx 2^3 xx 3^6)/(3^3 xx 5^2 xx 2^4 xx 3^2)` ...[∵ (a × b)m = am × bm]
= `(3^(4 + 6 - 3 - 2) xx 5^(4 - 2))/(2^(4 - 3))` ...`[∵ a^m/a^n = a^(m - n) and a^m xx a^n = a^(m + n)]`
= `(3^5 xx 5^2)/2`
= `(243 xx 25)/2`
= `6075/2`
APPEARS IN
RELATED QUESTIONS
Simplify and express the following in exponential form:
`(4^5 xx a^8b^3)/(4^5 xx a^5b^2)`
Simplify:
`(25 xx 5^2 xx t^8)/(10^3 xx t^4)`
Simplify and write the answer in the exponential form.
[(22)3 x 36] x 56
Simplify: `(2 xx 3^4 xx 2^5)/(9 xx 4^2)`
Simplify and express the following in exponential form:
`[(7/11)^5 ÷ (7/11)^2] xx (7/11)^2`
Simplify and express the following in exponential form:
(37 ÷ 35)4
Simplify and express the following in exponential form:
`[(3/5)^3 xx (3/5)^8] ÷ [(3/5)^2 xx (3/5)^4]`
Evaluate:
`(5^4 xx 7^4 xx 2^7)/(8 xx 49 xx 5^3)`
Evaluate:
`(125 xx 5^2 xx a^7)/(10^3 xx a^4)`
Evaluate:
`(3^4 xx 12^3 xx 36)/(2^5 xx 6^3)`
