Question

2 raised to the power of 2p=256

Answer 1

Answer:

p = 4

Step-by-step explanation:

2^2p=256

2^2p=2^8

2p=8

p=8/2

p=4

Answer 2

Answer:

The value of p is 4.

Explanation:

Given,

${2}^{2p} = 256$

$\implies {2}^{2p} = {2}^{8}$

If base is equal then, their powers are also equal.

$\implies \: if \: \: \: {a}^{m} = {a}^{n}$

$then \: : \: m = n$

Similarly , here,

$2p \: = \: 8$

$p = \frac{8}{2}$

$p = \cancel{ \frac{8}{2} }$

$\implies \: p = 4$

Therefore, here the value of p is 4.

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$how \: \: 256 \: \: \: = \: \: \: {2}^{8}$

$256 = 128 \times 2$

$256 = 64 \times 2 \times 2$

$256 = 32 \times 2 \times 2 \times 2$

$256 = 16 \times 2 \times 2 \times 2 \times 2$

$256 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 4$

$256 = {2}^{6} \times {2}^{2}$

$256 = {2}^{(6 + 2)}$

$256 = {2}^{8}$

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