Question

Evaluate the following:

`7^-4 xx (343)^(2/3) ÷ (49)^(-1/2)`

Answer 1

`7^-4 xx (343)^(2/3) ÷ (49)^(-1/2)`

= `7^-4 xx (7^3)^(2/3) ÷ (7^2)^(-1/2)`

= `7^-4 xx 7^(3 xx 2/3) ÷ 7^(2 xx (-1/2)`

= `7^-4 xx 7^2 ÷ 7^-1`

= `7^(-4 + 2 -(-1))`        ....(Using a^m x aⁿ = a^m+n and a^m ÷ aⁿ = a^m-n)

= `7^(-4 + 2 + 1)`

= 7^-1

= `(1)/(7)      ....("Using" "a"^-"m" = 1/"a"^"m")`.