Question

Using laws of exponents solve 1024 into 216

Answer 1

Step-by-step explanation:

Given that:Using laws of exponents solve 1024 into 216

To find: Solve this

Solution:

We know that

$1024 = {2}^{10} \\ 216 = {6}^{3}$

we know that 6= 2×3

$216 = {6}^{3} = ( {2 \times 3)}^{3}$

we know that

$\boxed{ {(a \times b)}^{n} = {a}^{n} \times {b}^{n}}$

Thus

$( {2 \times 3)}^{3} = {2}^{3} \times {3}^{3}$

Now multiply

$1024 \times 216 \\ \\ = {2}^{10} \times {2}^{3} \times {3}^{3} \\ \\ = {2}^{(10 + 3)} \times {3}^{3} \\ \\ \because \boxed{{a}^{n} \times {a}^{m} = {a}^{(m + n)}} \\ \\\bold{ 1024 \times 216 = {(2)}^{13} \times {3}^{3} } \\ \\ 1024 \times 216 = 221184$

Hope it helps you.

Answer 2

Answer:

1024×216=221184 ᴀɴsᴡᴇʀ ɪs ᴛʜɪs ᴏɴᴇ