Question

simply using laws of exponents​

Answer 1

QueStI0N -

Simplify things following -

$\sf{ { ( 27x ) } ^ { \frac{ -2}{3} } \times { ( 216 x ) } ^ {\frac{1}{3} } }$

Solution -

$\sf{ { ( 27x ) } ^ { \frac{ -2}{3} } \times { ( 216 x ) } ^ {\frac{1}{3} } } \\ \\ \sf{ => { ( 3x ) } ^ { 3 \times \frac{ -2}{3} } \times { ( 6x ) } ^ { 3 \times \frac{1}{3} } } \\ \\ \sf{ => { ( 3x ) } ^ { -2 } \times ( 6x ) } \\ \\ \sf{ => \dfrac{ 6x \times 9}{ x^2 } } \\ \\ \sf{ => \dfrac{ 54}{ x } } \\ \\ \sf{ \bold{ Answer \: - }} \\ \\ \sf{ \leadsto { \dfrac{ 54}{ x } }}$

Laws Of Exponents -

$\sf{ a^n \times a^m = a^ { m + n } } \\ \\ \sf{ \dfrac{ a^n}{ a^m} = a^ { m - n } } \\ \\ \sf{ a^0 = 1 } \\ \\ \sf{ {( a^m )}^n = a^ { mn } }$