Question

find the value of
(2/3)^4 *(1/3)^2

Answer 1

(2⁴/3⁴)*(1²/3²)
(16/81)(1/9)
16/729

Answer 2

$\bigg( \dfrac{2}{3} \bigg)^4 \times \bigg( \dfrac{1}{3} \bigg)^2$

Apply (a/b)ⁿ = aⁿ/bⁿ:

$= \dfrac{2^4}{3^4}\times \dfrac{1^2}{3^2}$

Put into single fraction:

$=\dfrac{2^4 \times 1^2}{3^4 \times 3^2}$

Apply: aⁿ x aˣ = aⁿ⁺ˣ:

$=\dfrac{2^4}{3^{4+2} }$

$=\dfrac{2^4}{3^6 }$

Evaluate the exponents:

$=\dfrac{16}{729}$