Question

18. Reduce a una sola potencia:

Answer 1

$a) {a}^{5} \times {a}^{3} = {a}^{5 + 3} = {a}^{8}$

$b) {x}^{4} \times {x}^{4} = {x}^{4 + 4} = {x}^{8}$

$c) {x}^{2} \times {x}^{8} = {x}^{2 + 8} = {x}^{10}$

$d) {a}^{8} \div {a}^{5} = {a}^{8 - 5} = {a}^{3}$

$e) {x}^{6} \div {x}^{5} = {x}^{6 - 5} = x$

$f) {( {a}^{3} )}^{2} = {a}^{3 \times 2} = {a}^{6}$

$g) {( {10}^{2} )}^{3} = {10}^{2 \times 3} = {10}^{6}$

$h) {( {m}^{2} )}^{4} = {m}^{2 \times 4} = {m}^{8}$

$i) {( {5}^{4} )}^{2} = {5}^{4 \times 2} = {5}^{8}$

$j) {a}^{3} \times {a}^{4} = {a}^{3 + 4} = {a}^{7}$

$k) {a}^{6} \div {a}^{4} = {a}^{6 - 4} = {a}^{2}$

$l)( {a}^{8} \div {a}^{6} ) \times ( {a}^{6} \div {a}^{5} ) = {a}^{8 - 6} \times {a}^{6 - 5} = {a}^{2} \times a = {a}^{2 + 1} = {a}^{3}$

$m)( {x}^{3} \times {x}^{5} ) \div ( {x}^{2} \times {x}^{4} ) = {x}^{3 + 5} \div {x}^{2 + 4} = {x}^{8} \div {x}^{6} = {x}^{ 8- 6} = {x}^{2}$

$n)( {a}^{2} \times {a}^{3} \times {a}^{2} ) \div ( {a}^{5} \times {a}^{2} ) = {a}^{2 + 3 + 2} \div {a}^{5 + 2} = {a}^{7} \div {a}^{7} = {a}^{7 - 7} = {a}^{0} = 1$

$o) {( {x}^{2} )}^{3} \div x = {x}^{2 \times 3} \div x = {x}^{6} \div x = {x}^{6 - 1} = {x}^{5}$

$p) {( {m}^{3} )}^{2} \div {m}^{4} = {m}^{3 \times 2} \div {m}^{4} = {m}^{6} \div {m}^{4} = {m}^{6 - 4} = {m}^{2}$

$q) {( {a}^{4} )}^{3} \div {( {a}^{3} )}^{3} = {a}^{4 \times 3} \div {a}^{3 \times 3} = {a}^{12} \div {a}^{9} = {a}^{12 - 9} = {a}^{3}$

$r) [ {( {a}^{3} )}^{2} \times {( {a}^{2} )}^{4} ] \div {( {a}^{5} )}^{2} = ( {a}^{3 \times 2} \times {a}^{2 \times 4} ) \div {a}^{5 \times 2} = ( {a}^{6} \times {a}^{8} ) \div {a}^{10} = {a}^{6 + 8} \div {a}^{10} = {a}^{14} \div {a}^{10} = {a}^{14 - 10} = {a}^{4}$