Question

simplify( 7)¹÷2×(7)3÷2​

Answer 1

Answer:

7÷3×7×3÷2

= 7÷63÷2

= 9÷2

= 4.5

Answer 2

Answer:

${\small{\bold{19. \ \ (7)^{1/2} × (7)^{3/2}}}}$

${\small{\tt{= (7)^{ 1/2 + 3/2} = (7)^{4/2} = 7^2 = 49}}}$

${\small{\bold{20. \ \ 2×(16)^{-1/4} × (81)^{1/2}}}}$

${\small{\tt{= 2 × (2^4)^{-1/4} × (9^2)^{1/2}}}}$

${\small{\tt{ = 2× \dfrac{1}{2} × 9 = 9}}}$

${\small{\bold{21. \: \: \: 4^x + 4^x + 4^x = 48}}}$

${\small{\tt{\implies{3(4^x) = 48}}}}$

${\small{\tt{\implies{4^x = \dfrac{48}{3}}}}}$

${\small{\tt{\implies{4^x = 16 = {4}^{2} }}}}$

${\small{\tt{\implies{x = 2}}}}$

${\small{\bold{22. \ \ 4 × (32)^{2/5} × (3)^{-2}}}}$

${\small{\tt{ \: = 4 × (2^5)^{2/5} × \bigg(\dfrac{1}{3} \bigg)^2}}}$

${\small{\tt{= 4× 2^2 × \dfrac{1}{9}}}}$

${\small{\tt{ = 4×4 × \dfrac{1}{9} = \dfrac{16}{9}}}}$

${\small{\bold{23. \ \ 2^{x-3} = 1}}}$

${\small{\tt{\implies{2^{x-3} = 2^0 \: \: \: \: \: \: \: \: \bigg\lbrace \because x^0 = 1 \bigg\rbrace}}}}$

${\small{\tt{\implies{x-3 = 0 \ \ \ \implies x = 3}}}}$

${\small{\bold{24. \ \ \ 2^{2x+2} = 4^{2x-1}}}}$

${\small{\tt{\implies{2^{2x+2} = (2^2)^{2x-1}}}}}$

${\small{\tt{\implies{2^{2x+2} = 2^{4x-2}}}}}$

${\small{\tt{\implies{ 2x + 2 = 4x - 2 }}}}$

${\small{\tt{\implies{4x-2x = 2+2}}}}$

${\small{\tt{\implies{2x = 4}}}}$

${\small{\tt{\implies{x= \dfrac{4}{2} = 2}}}}$