Answer:
∛27 = 3
Step-by-step explanation:
A radical is simply a fractional exponent: [tex]a^{(\frac{m}{n})} = \sqrt[n]{a^{m} }[/tex]
Hence, ∛27 = [tex]27^{(\frac{1}{3})}[/tex]
Since 27 = 3³, then:
You could rewrite ∛27 as ∛(3)³.
[tex]\sqrt[3]{3^{(3)} } = 3^{[(3)*(\frac{1}{3})]}[/tex]
Multiplying the fractional exponents (3 × 1/3) will result in 1 (because 3 is the multiplicative inverse of 1/3). The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as 1.
Therefore, ∛27 = 3.
