10. a) [tex] 3^{-2}+ 4^{-2}= \frac{1}{ 3^{2} }+ \frac{1}{ 4^{2} } = \frac{1}{9}+ \frac{1}{16}= \frac{16+9}{144}= \frac{25}{144} [/tex] ≈ 0.173611
b) [tex]2- \frac{3}{8}:(17-4 ^{2} )=2- \frac{3}{8}:(17-16)=2- \frac{3}{8}:1=2- \frac{3}{8} = \frac{16-3}{8} = \frac{13}{8} [/tex] ≈ [tex]1 \frac{5}{8} [/tex]; ≈ 1.625
c) [tex] 1^{-2}-(- \frac{6}{7}) ^{2}*49= 1-49* (-\frac{6}{7}) ^{2}= 1-49* (\frac{6}{7}) ^{2}= 1-49* \frac{36}{49}= [/tex][tex]1-36=-(36-1)=-35[/tex]
d) [tex](- \frac{1}{5} )^{-2}-7 ^{2}=(-5) ^{2} -49=25-49=-(49-25)=-24 [/tex]
e) [tex]1.7 ^{2} -0.3 ^{2} = (\frac{17}{10}) ^{2} -( \frac{3}{10}) ^{2}= \frac{289}{100}- \frac{9}{100}= \frac{289-9}{100}= \frac{280}{100}= \frac{14}{5} [/tex] ≈[tex]2 \frac{4}{5} [/tex]; 2.8
f) [tex]0.5 ^{2}- 3^{2}+ 0.2^{2} =( \frac{1}{2}) ^{2} -9+ (\frac{1}{5}) ^{2}= \frac{1}{4} -9+ \frac{1}{25}= \frac{25-900+4}{100}= \frac{-871}{100}= [/tex][tex]- \frac{871}{100} [/tex] ≈ [tex]-8 \frac{71}{100} [/tex]; ≈ -8.71
g) [tex](- \frac{2}{4}) ^{-1}+3 ^{3} - 1^{3}=(- \frac{1}{2}) ^{-1}+27-1=-2+27-1=-3+27=24 [/tex]
h) [tex]( \frac{1}{2}) ^{3} -0.5 ^{3} + 1^{-10}=( \frac{1}{2}) ^{3} -( \frac{1}{2}) ^{3} +1=1 [/tex]
i) [tex]25-25:(- \frac{3}{5}) ^{-2} = 25-25:( \frac{3}{5}) ^{-2}=25-25:( \frac{5}{3}) ^{2}=25-25:\frac{25}{9} [/tex][tex]=25-25* \frac{9}{25}=25-9=16 [/tex]
