Question

Simplify and choose the correct option.

(2^3 × 2)^2 = ?
(a) 2^6
(b) 2^3
(c) 2^8
(d) All of the above.​

Answer 1

Explanation:

`\dashrightarrow\sf{({2}^(3) * 2)}^(2)`

Using law of exponent
`{\bf{{a}^(m) * {a}^(n) = {a}^(m + n)}}`

`\dashrightarrow\sf{({2}^(3) * {2}^(1))}^(2)`

`\dashrightarrow\sf{({2}^(3+1))}^(2)`

`\dashrightarrow\sf{({2}^(4))}^(2)`

Again, using law of exponent
`{\bf{({a}^(m))^(n) = {a}^(mn)}}`

`\dashrightarrow\sf{({2}^(4))}^(2)`

`\dashrightarrow\sf{({2})^(4 * 2)}`

`\dashrightarrow\sf{({2})^(8)}`

`{\bigstar \: {\small\underline{\boxed{\sf{\red{Answer = (2)^8}}}}}}`

∴ The option (c) 2⁸ is the ur correct answer.

`\underline{\rule{200pt}{2.5pt}}`

Answer 2

(c) 2^8

Explanation:

Given: (2^3 × 2)^2

Rewrite: (2³ x 2)²

Cube: (8 x 2)²

Multiply: (16)²

Square: 256

(a) 2^6

`2^(6)` = 64 -> Not our answer

(b) 2^3

We can tell this isn't our answer as it is smaller than a, and a was too small

(c) 2^8

`2^(8)` = 256 -> 256 = 256 (from above) so this is our answer

(d) All of the above.​

Incorrect, it won't be "all the options" as only one can be correct in this scenario