Question

find the value of (2‐¹×4‐¹)÷2‐²​

Answer 1

Answer:

(2-¹×4-¹)÷2-²

= (1/2×1/4)÷1/2²

= 1/8÷1/4

= 1/8×4

= 1/2

= 2-¹

Answer 2

Correct question:

$\sf{ \mapsto \: find \: the \: value \: of} \: ({2}^{ - 1} \times {4}^{ - 1})\div{2}^{ - 2}$

Solution steps :

step 1 :

• we want to make 4 as 2² :

$\sf{\implies({2}^{ - 1} \times {4}^{ - 1})\div{2}^{ - 2}}$

$\sf{\implies({2}^{ - 1} \times {({2}^{2} )}^{ - 1})\div{2}^{ - 2}}$

step 2 :

• use the formula (aⁿ)ᵐ = aⁿ×ᵐ

$\sf{\implies({2}^{ - 1} \times {({2}^{2} )}^{ - 1})\div{2}^{ - 2}}$

$\sf{\implies({2}^{ - 1} \times({2}^{2 \times(-1)}))\div{2}^{ - 2}}$

$\sf{\implies({2}^{ - 1} \times{2}^{ - 2})\div{ {2}^{ - 2}}}$

step 3 :

• if we want to multiply 2 bases which are same there exponents should be added.

$\sf{\implies({2}^{ - 1} \times{2}^{ - 2})\div{ {2}^{ - 2}}}$

$\sf{\implies({2}^{( - 1) + ( - 2)})\div{ {2}^{ - 2}}}$

$\sf{\implies{2}^{ - 3}\div{ {2}^{ - 2}}}$

step 4 :

• same as multiplication if we want to divide 2 bases which are same there exponents should be subtracted.

$\sf{\implies{2}^{ - 3}\div{ {2}^{ - 2}}}$

$\sf{\implies{2}^{( - 3) - ( - 2)}}$

${\sf{\implies{2}^{ - 1}}}$

step 5 :

• use the formula : a^-x = 1/a^x

${\sf{\implies{2}^{ - 1}}}$

${\sf{\implies \dfrac{1}{{2}^{1}}}}$

${{\sf{\implies{\dfrac{1}{2}}}}}$

final answer:

$\huge \boxed{{\sf{\implies{\dfrac{1}{2}}}}}$