Question

evaluate (2-¹ × 4-¹)-¹ ÷ 2​

Answer 1

Answer:

${\sf{{\dfrac{1}{12}} }}$

Step-by-step explanation:

Given : ${\sf{\ \ (2^{- 1} \times 3^{- 1}) \div 2}}$

• ${\boxed{\sf{\red{Identity \ : \ a^{- 1} = {\dfrac{1}{a}}}}}}$

$\Rightarrow{\sf{ \left( {\dfrac{1}{2}} \times {\dfrac{1}{3}} \right) \div 2}}$

$\Rightarrow{\sf{ \left( {\dfrac{1}{2 \times 3}} \right) \div 2}}$

$\Rightarrow{\sf{ \left( {\dfrac{1}{6}} \right) \div 2}}$

$\Rightarrow{\sf{ \left( {\dfrac{1}{6}} \right) \times {\dfrac{1}{2}} }}$

$\Rightarrow{\sf{ {\dfrac{1}{6 \times 2}} }}$

$\Rightarrow{\boxed{\sf{{\dfrac{1}{12}} }}}$

Answer 2

Given,

(2-¹ × 4-¹)-¹ ÷ 2

we know that

$1</strong><strong>/</strong><strong> \: a {}^{k} = a {}^{ - k}$

Now,

(2-¹ × 4-¹)-¹ ÷ 2

=(1/2×1/4)-¹ ÷ 2

=(1/8)-¹÷2

=1/1/8 ×1/2

=8/1×1/2

=4