Question

The value of 3' x10, when x = -2, can be

written in simplest form as a lb, where
a=
and b =

Answer 1

a=-8 and b=-2

Explanation:

Edge

Answer 2

`a = 8` and
`b = 2`

Explanation:

Given

`\sqrt[3]{x^(10)}`

`x = -2`

Required

Express as:
`a\sqrt[3]{b}`

Substitute -2 for x in
`\sqrt[3]{x^(10)}`

`\sqrt[3]{x^(10)} = \sqrt[3]{(-2)^(10)}`

`\sqrt[3]{x^(10)} = \sqrt[3]{1024}`

Express 1024 as 2^10

`\sqrt[3]{x^(10)} = \sqrt[3]{2^(10)}`

Apply law of indices:

`\sqrt[3]{x^(10)} = \sqrt[3]{2^(9+1)}`

Apply law of indices: Split

`\sqrt[3]{x^(10)} = \sqrt[3]{2^(9)*2^1}}`

`\sqrt[3]{x^(10)} = \sqrt[3]{2^(9)} *\sqrt[3]{2^1}}`

`\sqrt[3]{x^(10)} = \sqrt[3]{2^(9)} *\sqrt[3]{2}}`

`\sqrt[3]{x^(10)} = 2^{9*(1)/(3)}} *\sqrt[3]{2}}`

`\sqrt[3]{x^(10)} = 2^3 *\sqrt[3]{2}}`

`\sqrt[3]{x^(10)} = 8\sqrt[3]{2}}`

By comparison:

`a = 8` and
`b = 2`