The fourth root of ⁴√(81x³y⁴z⁸)with rational exponents is [tex]3x^{\frac{3}{4} }yz^{2}[/tex]
How to find the fourth root of ⁴√(81x³y⁴z⁸)
To find the fourth root of ⁴√(81x³y⁴z⁸) with rational exponents, we use the root rule of indices which states that [tex]\sqrt[n]{a} = a^{\frac{1}{n} }[/tex]
So, ⁴√(81x³y⁴z⁸) = ⁴√(81 × ⁴√x³ × ⁴√y⁴ × ⁴√z⁸)
We now apply the
So, ⁴√(81x³y⁴z⁸) = ⁴√81 × ⁴√x³ × ⁴√y⁴ × ⁴√z⁸
[tex]= 3 X x^{\frac{3}{4} } X y^{\frac{4}{4} } X z^{\frac{8}{4} } \\= 3 X x^{\frac{3}{4} } X y^{1} X z^{2} \\= 3x^{\frac{3}{4} }yz^{2}[/tex]
So, the fourth root of ⁴√(81x³y⁴z⁸)with rational exponents is [tex]3x^{\frac{3}{4} }yz^{2}[/tex]
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