Question

Laws Of IndiciesCan someone please help me with this?​

Answer 1

Answer:

See below

Step-by-step explanation:

$1) : {a}^{5} {b}^{4} {c}^{3} \div {a}^{2} {b}^{3} c \\ \\ = {a}^{5 - 2} {b}^{4 - 3} {c}^{3 - 1} \\ \\ = {a}^{3} {b}^{1} {c}^{2} \\ \\ = {a}^{3} {b} {c}^{2} \\ \\ \\2)\: (x^2 y^3)^3\\\\= x^{2\times 3}y^{3\times 3}\\\|= x^{6}y^{9}\\\\\\3)\:5 {a}^{4} \div ( {a}^{2} \times 3a) \\ \\ = 5 {a}^{4} \div (3 {a}^{2 + 1} ) \\ \\ = 5 {a}^{4} \div (3 {a}^{3} ) \\ \\ = \frac{5}{3} {a}^{4 - 3} \\ \\ = \frac{5}{3} {a} \\ \\ \\ 4)\: \frac{14 {a}^{5} }{2 {a}^{3} \times 7 {a}^{4} } \\ \\ = \frac{14 {a}^{5} }{2 \times 7 {a}^{3 + 4} } \\ \\ = \frac{ \cancel{14} {a}^{5} }{ \cancel{14}{a}^{3 + 4} } \\ \\ = \frac{ {a}^{5} }{ {a}^{7} } \\ \\ = {a}^{5 - 7} \\ \\ = {a}^{ - 2} \\ \\ = \frac{1}{{a}^{2} }$

Answer 2

Answer:

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.    $5a^{4}:(a^{2}*3a)=\frac{5a^{4} }{a^{2}*3a } =\frac{5a^{2} }{3a} =\frac{5a}{3}$

4.    $\frac{14a^{5}} {2a^{3}*7a^{4}} =\frac{2a}{2a^{3} }=\frac{1}{a^{2} }$