Justify \sqrt[3]{8} * \sqrt[3]{8} = 16using the properties of exponents in at least two different ways.

Swetank asked Oct 15, 2023

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35 votes

Justify
$\sqrt[3]{8} * \sqrt[3]{8} = 16$ using the properties of exponents in at least two different ways.

$Justify \sqrt[3]{8} * \sqrt[3]{8} = 16using the properties of exponents in at least-example-1$

Swetank asked Oct 15, 2023

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13 votes

EXPLANATION

Given the cubic root:

$\sqrt[3]{8}\cdot\sqrt[3]{8}$

Rewriting 8 as 2^3:

$=\sqrt[3]{2^3}\cdot\sqrt[3]{2^3}$

Applying the property of roots:

$\sqrt[3]{a^3}=a$

$=2\cdot2=4$
$\sqrt[3]{8}\cdot\sqrt[3]{8}=\sqrt[3]{8^2}=\sqrt[3]{64}=4$

Ender Look answered Oct 22, 2023

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