Question

Find
[(4/7) ^ 2] ^ - 3 × [7/4] ^ 5​

Answer 1

Step-by-step explanation:

= [(4/7)^2]^-3 × [7/4]^5

= [(4²/7²)^-3] x (7⁵/4⁵)

= (7²/4²)³ × (7⁵/4⁵)

= (7⁶/4⁶) × (7⁵/4⁵)

= (7/4)⁶ × (7/4)⁵

= (7/4)^6+5

= (7/4)¹¹

Answer 2

Given :

• ${\sf{\bigg[\bigg(\dfrac{4}{7}\bigg)^2\bigg]^{- 3}~×~\bigg[\dfrac{7}{4}\bigg]^5}}$

$~$

Solution :

$\qquad{\sf:\implies{\bigg[\bigg(\dfrac{4}{7}\bigg)^2\bigg]^{- 3}~×~\bigg[\dfrac{7}{4}\bigg]^5}}$

$\qquad{\sf:\implies{\bigg[\bigg(\dfrac{4^2}{7^2}\bigg)^{- 3}\bigg]~×~\bigg(\dfrac{7^5}{4^5}\bigg)}}$

$\qquad{\sf:\implies{\bigg(\dfrac{7^2}{4^2}\bigg)^3~×~\bigg(\dfrac{7^5}{4^5}\bigg)}}$

$\qquad{\sf:\implies{\bigg(\dfrac{7^6}{4^6}\bigg)~×~\bigg(\dfrac{7^5}{4^5}\bigg)}}$

$\qquad{\sf:\implies{\bigg(\dfrac{7}{4}\bigg)^6~×~\bigg(\dfrac{7}{4}\bigg)^5}}$

$\qquad{\sf:\implies{\bigg(\dfrac{7}{4}\bigg)^{6~+~5}}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{\bigg(\dfrac{7}{4}\bigg)^{11}}}}}}}$★

$~$

Hence,

• The value is (7/4)¹¹.