Question

Laws Of Indicies
Can someone please help me with this?​

Answer 1

1.
`a^(5) b^(4)c^(3):a^(2)b^(3)c=a^(3)bc^(2)`

2.
`(x^(2)y^(3))^(3) =(x^(2) )^(3)(y^(3))^(3)=x^(6)y^(9)`

3.
`5a^(4):(a^(2)*3a)=(5a^(4) )/(a^(2)*3a ) =(5a^(2) )/(3a) =(5a)/(3)`

4.
`\frac{14a^(5)} {2a^(3)*7a^(4)} =(2a)/(2a^(3) )=(1)/(a^(2) )`

Answer 2

See below

Explanation:

`1) : {a}^(5) {b}^(4) {c}^(3) / {a}^(2) {b}^(3) c \\ \\ = {a}^(5 - 2) {b}^(4 - 3) {c}^(3 - 1) \\ \\ = {a}^(3) {b}^(1) {c}^(2) \\ \\ = {a}^(3) {b} {c}^(2) \\ \\ \\</p><p></p><p>2)\: (x^2 y^3)^3\\\\</p><p>= x^(2* 3)y^(3* 3)\\\|</p><p></p><p>= x^(6)y^(9)\\\\\\</p><p></p><p></p><p></p><p>3)\:5 {a}^(4) / ( {a}^(2) * 3a) \\ \\ = 5 {a}^(4) / (3 {a}^(2 + 1) ) \\ \\ = 5 {a}^(4) / (3 {a}^(3) ) \\ \\ = (5)/(3) {a}^(4 - 3) \\ \\ = (5)/(3) {a} \\ \\ \\ </p><p></p><p></p><p>4)\: \frac{14 {a}^(5) }{2 {a}^(3) * 7 {a}^(4) } \\ \\ = \frac{14 {a}^(5) }{2 * 7 {a}^(3 + 4) } \\ \\ = \frac{ \cancel{14} {a}^(5) }{ \cancel{14}{a}^(3 + 4) } \\ \\ = \frac{ {a}^(5) }{ {a}^(7) } \\ \\ = {a}^(5 - 7) \\ \\ = {a}^( - 2) \\ \\ = \frac{1}{{a}^(2) } \\ \\`