Question

2 to the power of 30 + 2 to the power of 29 + 2 to the power of 28 divided by 2 to the power of 31 + 2 to the power of 30 - 2 to the power of 29 is equals to 7 divided by 10 prove that

Answer 1

(2^30+2^29+2^28)/(2^31+2^30-2^29)=(2^29*2^1+2^29+2^29/2^1)/(2^29*2^2+2^29*2^1-2^29)=
[2^29(2+1+1/2)]/[2^29(4+2-1)]=(3+1/2)/5=7/10
                                  
                                Hence proved.

Answer 2

Step-by-step explanation:

$\bf \underline{Prove\: that-}$

$\sf\dfrac{ {2}^{30} + {2}^{29} + {2}^{28} }{ {2}^{31} + {2}^{30} - {2}^{29} } = \dfrac{7}{10}$

$\bf \underline{Solution-}$

${~~~~~~:~~~\implies\sf\dfrac{ {2}^{30} + {2}^{29} + {2}^{28} }{ {2}^{31} + {2}^{30} - {2}^{29} } = \dfrac{7}{10} }$

$\textsf{Taking 2²⁸ Common }$

$\\{~~~~~~:~~~\implies\sf\dfrac{ {2}^{28}( {2}^{2} + {2}^{1} + {2}^{0} )}{ {2}^{28} ({2}^{3} + {2}^{2} - {2}^{1}) } = \dfrac{7}{10} }$

$\\{~~~~~~:~~~\implies\sf\dfrac{ \cancel{{2}^{28}}( 4 + 2 + 1 )}{ \cancel{{2}^{28} }(8 + 4 - 2) } = \dfrac{7}{10} }$

$\\{~~~~~~:~~~\implies\sf\dfrac{ 1 \times 7}{ 1(12 - 2) } = \dfrac{7}{10} }$

$\\{~~~~~~:~~~\implies\sf\dfrac{ 7}{ 10} = \dfrac{7}{10} }$

$\textsf{LHS = RHS}$

$\bf \underline{Hence\: proved.}$