1
[tex] \frac{5 {}^{7} \times 5 {}^{2} \times 5 {}^{ - 3} }{5 {}^{3} \times 5 {}^{2} } = \frac{5 {}^{7 + 2 - 3} }{5 {}^{3 + 2} } = \frac{5 {}^{6} }{5 {}^{5} } = 5{}^{6 - 5} = 5 {}^{1} = 5 \\ [/tex]
2
[tex] - \sqrt{125} + 9 \sqrt{5} - \sqrt{720} \\ = - 5 \sqrt{5} + 9 \sqrt{5} - 12 \sqrt{5} \\ = - 8 \sqrt{5} \\ [/tex]
3
[tex]0.00000056 = 5.6 \times 10 {}^{ - 7} \\ \\ 2.500.000.000 = 2.5 \times 10 {}^{9} [/tex]
4
[tex] \frac{5}{ \sqrt{3} + \sqrt{7} } = \frac{5}{ \sqrt{3} + \sqrt{7} } \times \frac{ \sqrt{3} - \sqrt{7} }{ \sqrt{3} - \sqrt{7} } \\ = \frac{5 \sqrt{3} - 5 \sqrt{7} }{3 - 7} \\ = - \frac{5 \sqrt{3} - 5 \sqrt{7} }{4} [/tex]
5
[tex]3 {}^{n} = 243 \\ n = \sqrt[3]{243} \\ n = 5[/tex]
[tex]4 {}^{n} = ( - 2) {}^{0} \\ 4 {}^{n} = 1 \\ n = 0[/tex]
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