Question

Calculate:

`3^(14/3) xx 5^((-4)/3) xx 15^((-2)/3)`

Answer 1

Given,

`3^(14/3) xx 5^((-4)/3) xx 15^((-2)/3)`

We need to simplify the given terms.

Thus, `3^(14/3) xx 5^((-4)/3) xx 15^((-2)/3)`

⇒ `3^((18/3 + (-4)/3)) xx 5^((-4)/3) xx 15^((-2)/3)`

⇒ `3^(18/3) xx 3^((-4)/3) xx 5^((-4)/3) xx 15^((-2)/3)`

If powers are same and multiplied the base. i.e, aⁿ × bⁿ = (a × b)ⁿ

⇒ `3^6 xx (15)^((-4)/3) xx (15)^((-2)/3)`

⇒ `3^6 xx (15)^((-4)/3 - 2/3)`  ...[∴ aⁿ × a^m = a^{n + m}]

⇒ `3^6 xx (15)^((-6)/3)`

⇒ `3^6 xx (15)^-2`

⇒ `3^6 xx (3 xx 5)^-2`  ...[∴ aⁿ × bⁿ = (a × b)ⁿ]

⇒ `3^6 xx 3^-2 xx 5^-2`  ...[∴ aⁿ × a^m = a^{n + m}]

⇒ `3^4 xx 5^-2`   ...`[∴ a^-n = 1/a^n]`

= `3^4/5^2`

= `81/25`

Hence, the required is `81/25`.