Question

Work out the value of "n"

Answer 1

Answer:

${ \tt{ \frac{1}{16} \div \sqrt[3]{2} = {2}^{n} }} \\ \\ { \tt{\frac{1}{16} \times \frac{1}{ {2}^{ \frac{1}{3} } } = {2}^{n} }} \\ \\ { \tt{ \frac{1}{ {2}^{4} } \times \frac{1}{ {2}^{ \frac{1}{3} } } = {2}^{n} }}$

• from law of indices:

${ \boxed{ \rm{ \frac{1}{ {a}^{x} } = {a}^{ - x} }}}$

→ therefore:

${ \tt{ {2}^{ - 4} \times {2}^{ - \frac{1}{3} } = {2}^{n} }}$

• from law of indices:

${ \boxed{ \rm{ {a}^{k} \times {a}^{y} = {a}^{(k + y)} }}}$

→ therefore:

${ \tt{ {2}^{( - 4 - \frac{1}{3} )} = {2}^{n} }} \\ \\ { \tt{ - 4 - \frac{1}{3} = n }} \\ \\ { \tt{n = - 4 \frac{1}{3} }}$