Question

${2}^{4} . \: {2}^{ - 2}$
Answer is 4
I want explanation.​

Answer 1

Given:

• $\large{\sf{2⁴×2^{-2}}}$

Solution:

$\huge{\boxed{\large{\sf{\red{~~~~~~~~~~~~~~~~~Method\:1~~~~~~~~~~~~~~~~}}}}}$

We have given statement is $\large{\sf{2⁴×2^{-2}}}$.

We know that:

• $\large{\sf{a^{-n}\:=\:\bigg({\dfrac{1}{a}\bigg)^{n}}}}$

Therefore,

• $\large{\sf{2^{-2}\:=\:\bigg({\dfrac{1}{2}\bigg)^{2}}}}$

Now,

$\large{\sf{2⁴×\bigg(\dfrac{1}{2}\bigg)^{2}}}$

$\implies\large\sf{16×\dfrac{1}{4}}$

$\implies\large\sf{\cancel{16}×\dfrac{1}{\cancel{4}}}$

$\implies\large\sf{4 × 1}$

${\green{\implies{\large{\sf{2⁴×2^{-2}\:=\: 4}}}}}$

_____________________

$\huge{\boxed{\large{\sf{\red{~~~~~~~~~~~~~~~~~Method\:2~~~~~~~~~~~~~~~~~}}}}}$

We have given that $\large{\sf{2⁴×2^{-2}}}$. Here, both number are same in base.

We know that :

• $\large{\sf{a^{n}×a^{m}\:=\: a^{n+m}}}$

Therefore,

$\large{\sf{2⁴×2^{-2}}}$

$\implies\large{\sf{2^{4+(-2)}}}$

$\implies\large\sf{2^{4-2}}$

$\implies\large\sf{2²}$

${\green{\implies{\large{\sf{2⁴×2^{-2}\:=\: 4}}}}}$

Answer 2

Answer:

4

Step-by-step explanation:

2⁴*2-²

=2⁴*(1/2)²

=16*1/4

=16 is reduced by 4 by 4 times.

=4*1

=4.