Question

simplify and Express the result in power notation with positive exponent [{(8/9) ^-2}^1/3]6​

Answer 1

Answer:

$[[{(\frac{8}{9} )^{-2}}}]^{\frac{1}{3} }]^6= (\frac{9}{8} )^4$

Step-by-step explanation:

$(a^m)^n = a ^{m \times n}$

Also $( \frac{a}{b} )^{-n} =(\frac{b}{a} )^n$

$[[{(\frac{8}{9} )^{-2}}}]^{\frac{1}{3} }]^6\\= [{(\frac{8}{9} )^{-2}}}]^{\frac{1}{3} \times 6}\\= [{(\frac{8}{9} )^{-2}}}]^ 2}\\= {(\frac{8}{9} )^{-4}} \\= (\frac{9}{8} )^4$