Question

. If (2^3)^2 = 4n , then find n
(solve using steps)​

Answer 1

Answer:

(2^3)^2 =4n

2^(3×2) = 4n

2^6 = 2^2×n

n × 2^2 = 2^6

n = 2^6/2^2

n = 2^(6-2)

n = 2^4

n = 16

Answer 2

$\huge \fcolorbox{red}{green}{ \bf \blue{n = 3}}$

Step-by-step explanation:

Given -

• (2³)² = 4ⁿ

_____________________

To find -

• The value of n

_____________________

Solution -

$( {2}^{3} {)}^{2} = {4}^{n} \\ \\ = > {2}^{3 \times 2} = {(4)}^{n} \\ \\ = > {2}^{6} = ( {2}^{2} {)}^{n} \\ \\ = > {2}^{6} = {2}^{2 \times n} \\ \\ = > 6 = 2 \times n \\ \\ = > \cancel { \frac{6}{2} {}}^{ \: \: 3} = n \\ \\ = > n = 3$

SO,

THE VALUE OF 'n' IS 3.

____________________

Formulas we used -

When bases are same (as here x),

$( {x}^{m} {)}^{n} = {x}^{m \times n} \\ \\when \: \\ {x}^{m} = {x}^{n} \\ then \\ m = n$

More Formulas we should remember for these type of calculations :-

${x}^{m} \times {x}^{n} = {x}^{m + n} \\ {x}^{m} \div {x}^{n} = {x}^{m - n}$