The equivalent expression of [tex]\frac{2^4}{\sqrt[3]{xy}}[/tex] is [tex]\frac{\sqrt[3]{\frac{2^{12}}{xy}}}[/tex]
How to rewrite the expression?
The expression is given as:
[tex]\frac{2^4}{\sqrt[3]{xy}}[/tex]
Multiply 4 by 1
[tex]\frac{2^{4 * 1}}{\sqrt[3]{xy}}[/tex]
Express 1 as 3/3
[tex]\frac{2^{4 * 3/3}}{\sqrt[3]{xy}}[/tex]
Evaluate the product
[tex]\frac{2^{12 * 1/3}}{\sqrt[3]{xy}}[/tex]
Apply the following law of indices
[tex]a^\frac 1n = \sqrt[n]{a}[/tex]
So, we have:
[tex]\frac{\sqrt[3]{2}^{12}}{\sqrt[3]{xy}}[/tex]
The numerator and the denominator have the same root
So, we have:
[tex]\frac{\sqrt[3]{\frac{2^{12}}{xy}}}[/tex]
Hence, the equivalent expression of [tex]\frac{2^4}{\sqrt[3]{xy}}[/tex] is [tex]\frac{\sqrt[3]{\frac{2^{12}}{xy}}}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/24242989
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