How do you simplify $(4/81)^(3/2)$ ?

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Answer 1 · 2016-10-05T09:28:09

$(4/81)^(3/2)=8/729$

We use here the identities $(a/b)^m=a^m/b^m$ and $(a^m)^n=a^((mxxn))$

Hence $(4/81)^(3/2)$

= $((2xx2)/(3xx3xx3xx3))^(3/2)$

= $(2^2/3^4)^(3/2)$

= $(2^2)^(3/2)/(3^4)^(3/2)$ - using $(a/b)^m=a^m/b^m$

= $2^((2xx3/2))/(3^((4xx3/2))$ - using $(a^m)^n=a^((mxxn))$

= $2^3/3^6$

= $(2xx2xx2)/(3xx3xx3xx3xx3xx3)$

= $8/729$

How do you simplify (4/81)^(3/2)(4/81)^(3/2)?