Răspuns:
[tex]a) {n}^{2} = 49 \\ {n}^{2} = {7}^{2} \: \: n = 7 \\ b) {n}^{2} = 900 \\ {n}^{2} = {30}^{2} \: \: n = 30[/tex]
[tex]c) {n}^{3} = 64 \\ {n}^{3} = {4}^{3} \: \: n = 4 \\ d) {n}^{3} = 125 \\ {n}^{3} = {5}^{3} \: \: n = 5[/tex]
[tex] {n}^{3} = 1000 \\ {n}^{3} = {10}^{3} \: \: \: n = 10 \\ f) {6}^{2} + {n}^{2} = {10}^{2} \\ {n}^{2} = {10}^{2} - {6}^{2} \\ {n}^{2} = 100 - 36 \\ {n}^{2} = 64 \\ {n}^{2} = {8}^{2} \: \: \: n = 8[/tex]
[tex]g) {12}^{2} + {n}^{2} = {13}^{2} \\ {n}^{2} = {13}^{2} - {12}^{2} \\ {n}^{2} = 169 - 144 \\ {n}^{2} = 25 \\ {n}^{2} = {5}^{2} \: \: \: n = 5[/tex]
[tex]h) {n}^{2} - {5}^{2} = {12}^{2} \\ {n}^{2} = 144 + 25 \\ {n}^{2} = 169 \\ {n}^{2} = {13}^{2} \: \: n = 13[/tex]
[tex] i){n}^{2} \div {3}^{2} = {4}^{2} \\ {n}^{2} = 16 \times 9 \\ {n}^{2} = 144 \\ {n}^{2} = {12}^{2} \\ n = 12[/tex]
[tex]j)576 \div n = {2}^{4} \times {3}^{2} \\ 576 \div n = 16 \times 9 \\ 576 \div n = 144 \\ n = 576 \div 144 \\ n = {24}^{2} \div {12}^{2} \\ n = {(24 \div 12)}^{2} = {2}^{2} = 4[/tex]
[tex]k)n - {3}^{3} = {6}^{3} \\ n = 216 + 27 \\ n = 243[/tex]
[tex]l) { ({3}^{2} )}^{n + 2} = {3}^{n} \times {3}^{8} \\ {3}^{2n + 4} = {3}^{n} \times {3}^{8} \\ {3}^{2n} \times {3}^{4} = {3}^{n } \times {3}^{8} \\ {3}^{2n} = ({3}^{n} \times {3}^{8} )\div {3}^{4} \\ {3}^{2n} = {3}^{n} \times {3}^{4} \\ {3}^{2n} \div {3}^{n} = {3}^{4} \\ {3}^{n} = {3}^{4} \\ n = 4[/tex]
