Question

If a/b=(-3/7)^9÷(-3/7)^8,the value of (a/b)³ is​

Answer 1

Step-by-step explanation:

find the attachment and hope u understand this

Answer 2

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf \large\longmapsto \dfrac{a}{b} = { \bigg( \dfrac{ - 3}{7} \bigg)}^{9} \div { \bigg( \dfrac{ - 3}{7} \bigg)}^{8}$

Concept

When bases are same then powers gets added during multiplication and gets substracted during division.

$\sf \boxed{\bold{ \red{ \dfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }}}$

$\sf \boxed{\bold{ \red{ {a}^{m} \times {a}^{n} = {a}^{m + n} }}}$

$\sf \dfrac{a}{b} = { \bigg( \dfrac{ - 3}{7} \bigg)}^{9 - 8} = { \bigg( \dfrac{ - 3}{7} \bigg)}$

Now,we have to find (a/b)³

$\sf \longmapsto { \bigg(\dfrac{a}{b} \bigg) }^{3} = { \bigg( \dfrac{ - 3}{7} \bigg)}^{3}$

=>Now, expanding the powers so that we find the value of (a/b)³

$\sf \longmapsto { \bigg(\dfrac{a}{b} \bigg) }^{3} = { \bigg( \dfrac{ - 3}{7} \bigg)} \times { \bigg( \dfrac{ - 3}{7} \bigg)} \times { \bigg( \dfrac{ - 3}{7} \bigg)}$

$\sf \longmapsto { \bigg(\dfrac{a}{b} \bigg) }^{3} = \dfrac{ - 27}{343}$