The value of 3' x10, when x = -2, can be written in simplest form as a lb, where a= and b =

Question

asked Jan 13, 2022 209k views

2 Answers

Palme · Answer 1 · 2022-01-17T08:27:53+0000

Answer:

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