Question

2 power minus 1 x 4 power minus 1 divided by 2 power minus 2​

Answer 1

(2^-1) x (4^-1) / (2^-2)
USING LAW OF EXPONENTS- (A^-m)=(1/A)^m

[(1/2)^1] x [(1/4)^1] / [(1/2)^2]
1/2 x (1/4) / (1/4)

USING BODMAS
1/2 x [ (1/4) / (1/4) ]
1/2 x [ (1/4) x 4 ]
1/2 x 1
=> 1/2

Answer 2

The answer is 2⁻¹

GIVEN

2⁻¹ × 4⁻¹ ÷ 2⁻²

TO FIND

The value of given expression

SOLUTION

We can simply solve the above problem as follows;

We are given an expression;

2⁻¹ × 4⁻¹ ÷ 2⁻²

We can also write it as;

$\frac{ {2}^{ - 1} \times {4}^{ - 1} }{ {2}^{ - 2} }$

We can write 4⁻¹ as (2²)⁻¹

Applying;

(aᵐ)ⁿ = aᵐˣⁿ

Therefore,

(2²)⁻¹ = 2²ˣ⁻¹ = 2⁻²

We know that,

a⁻ⁿ = 1/aⁿ

Now,

$= \frac{2^{2} }{2^{1} \times {2}^{2} }$

We can also write it as;

$= \frac{2 \times 2}{2 \times 2 \times 2}$

=

$\frac{1}{2} = {2}^{ - 1}$

Hence, The answer is 2⁻¹

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