Which expression is equivalent to 4√81/16a^8b^12c^16?

To do roots of numbers with indices, divide the indice by the root. 4th root of [tex] a^{8} [/tex] is [tex] a^{\frac{8}{4}} [/tex] 4th root of [tex] b^{12} [/tex] is [tex] b^{ \frac{12}{4} } [/tex] 4th root of [tex] c^{16} [/tex] is [tex] b^{ \frac{16}{4}} [/tex] 4th root of 81 is 3 4th root of 16 is 2 [tex] \frac{3}{2} [/tex][tex] a^{2} [/tex][tex] b^{3} [/tex][tex] c^{4} [/tex]

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MrRoyal MrRoyal · Answer 2 · 2022-06-22T11:52:51+02:00

The equivalent expression of [tex]\sqrt[4]{\frac{81}{16}a^8b^{12}c^{16}}[/tex] is [tex]\frac{3}{2}(a^2b^3c^4)[/tex]

How to determine equivalent expression?

The expression is given as:

[tex]\sqrt[4]{\frac{81}{16}a^8b^{12}c^{16}}[/tex]

Take the 4th root of 81 and 16

[tex]\frac{3}{2}\sqrt[4]{a^8b^{12}c^{16}}[/tex]

Apply the law of indices on the above expression

[tex]\frac{3}{2}(a^{8/4}b^{12/4}c^{16/4}}[/tex]

Evaluate

[tex]\frac{3}{2}(a^2b^3c^4)[/tex]

Hence, the equivalent expression of [tex]\sqrt[4]{\frac{81}{16}a^8b^{12}c^{16}}[/tex] is [tex]\frac{3}{2}(a^2b^3c^4)[/tex]

Read more about equivalent expression at:

https://brainly.com/question/2972832

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