Question

Simplify

32x^8 ÷ 8x^32

Answer 1

Hello,

`\frac{32 {x}^(8) }{8x {}^(32) } = \frac{4 * 8 * x {}^(8) }{8x {}^(32) } = \frac{4x {}^(8) }{x {}^(32) } = 4x { }^(8 - 32) = 4x {}^( - 24)`

Answer 2

`\red{4 {x}^( - 24) }`

Explanation:

We know that,

`{a}^(m) * {a}^(m) = {a}^(m + n) \\ \\ \frac{ {a}^(m) }{ {a}^(n) } = {a}^(m - n) \: \: \: \: \: \: \: \: \: \: \: \\ \\ ({a}^(m))^(n) = {a}^(mn) \: \: \: \: \: \: \: \: \: \:`

Now using the above knowledge let us solve the sum.

`\frac{32 {x}^(8) }{8 {x}^(32) } \\ ( (32)/(8) ) * ( \frac{ {x}^(8) }{ {x}^(32) } ) \\ 4 * {x}^(8 - 32) \\ 4 * {x}^( - 24) \\ = 4 {x}^( - 24)`