Question

Simplify === 64 to the power -1/3(64 to the power 1/3 - 64 to the power 2/3.​

Answer 1

Answer:

answer no.1 - 4

answer no.2-8

Answer 2

Step-by-step explanation:

$\bf \underline{Given-}$

$\sf{ {64}^{ - \frac{1}{3} } \bigg [ {64}^{ \frac{1}{3} } - {64}^{ \frac{2}{3} } \bigg ] }$

$\bf \underline{To \: find-}$

$\textsf{Simplify the given fractional expression and find their value.}$

$\bf \underline{Solution-}$

$\textsf{Given fractional expression,}$

$\sf{ {64}^{ - \frac{1}{3} } \bigg [ {64}^{ \frac{1}{3} } - {64}^{ \frac{2}{3} } \bigg ] }$

$\sf{ \Rightarrow \:( {4}^{3} {)}^{ - \frac{1}{3} } \bigg[( {4}^{3} {)}^{ \frac{1}{3} } - ( {4}^{3} {)}^{ \frac{2}{3} } \bigg] }$

$\sf{ \Rightarrow \: {4}^{ \cancel3 \times \big( - \frac{1}{ \cancel3} \big) } \bigg( {4}^{ \cancel3 \times \frac{1}{ \cancel3} } - {4}^{ \cancel3 \times \frac{2}{ \cancel3} } \bigg) }$

$\sf{ \Rightarrow \: {4}^{ - 1} (4 - {4}^{2}) }$

$\sf{ \Rightarrow \: \frac{1}{4} (4 - {4}^{2} )}$

$\sf{ \Rightarrow \: \frac{1}{4} (4 - 16) }$

$\sf{ \Rightarrow \: \frac{1}{ \cancel4} \times ( - \cancel{ {12}}^{3} )}$

$\sf{ \Rightarrow \: - 3}$

$\bf \underline{Answer-}$

$\bf{ \underline{Hence \: after \: simplifying \: we \: get \: the \: value \: of : }}$

$\sf \underline{\boxed{ \sf{ {64}^{ - \frac{1}{3} } \bigg [ {64}^{ \frac{1}{3} } - {64}^{ \frac{2}{3} } \bigg ] } \: is \: -3 } }$