Evaluate the following.

a. $ \left[\frac{1}{9}\right]^{-1}-3 \div(9)^{-2} $

b. $ \left[4^{-1}-6^{-1}\right]^{-2} $

c. $ \left(\frac{11}{13}\right)^{3} \times 13 \times\left(\frac{11}{13}\right)^{-2} $

Solution:

a)  $ \left[\frac{1}{9}\right]^{-1}-3 \div(9)^{-2} $

= $9 - 3 \times 9^2$

=$ 9 - 3 \times 81$  =$ 9 - 243$ = $-234$ Answer

b)  $ \left[4^{-1}-6^{-1}\right]^{-2} $

= $\frac{1}{4} - \frac{1}{6}^{-2}$

= $\frac{1}{12}^{-2}$

= $12^2$

= $12 \times 12 = 144$ Answer

c) $ \left(\frac{11}{13}\right)^{3} \times 13 \times\left(\frac{11}{13}\right)^{-2} $

=  $(\frac{11}{13})^{3-2} \times 13$

= $(\frac{11}{13}^)1 \times 13$

= $\frac{11}{13} \times 13$ = 11 Answer 

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Updated on: 10-Oct-2022

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