Question

(81/16)^-3/4 find the multiplicative inverse

Answer 1

pls check the pic for answer.


Hope you got it!!

Answer 2

Answer:

$Multiplicative \:inverse\\ \:of \:\big(\frac{81}{16}\big)^{\left(\frac{-3}{4}\right)}\\=\big(\frac{3}{2}\big)^{3}\\=\frac{27}{8}$

Step-by-step explanation:

$\big(\frac{81}{16}\big)^{\left(\frac{-3}{4}\right)}\\=\big(\frac{3^{4}}{2^{4}}\big)^{\left(\frac{-3}{4}\right)}\\=\big(\frac{3}{2}\big)^{\left(4\times \frac{-3}{4}\right)}\\=\big(\frac{3}{2}\big)^{-3}$

Now,

$Multiplicative \:inverse\\ \:of \:\big(\frac{81}{16}\big)^{\left(\frac{-3}{4}\right)}\\=\big(\frac{3}{2}\big)^{3}$

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