Evaluate the followinga) b) $[4^{-1}-6^{-1}{]}^{-2}$c) $(\frac{11}{13}{)}^3\times 3\times (\frac{11}{13}{)}^{-2}$"

Solution:

a)$(\frac{1}{9})^{-1}-\frac{3 }{9^{-2}}$  

=$ 9 - 3 \times 9^{2}$

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

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

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

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

= $12^2$

= 12 $\times$ 12 = 144 

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

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

= $\left(\frac{11}{13}\right)^{1} \times 13$

=  11 

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Updated on: 10-Oct-2022

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