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What is the simplified value of the exponential expression [tex]27^{\frac{1}{3}}[/tex]?

A. [tex]\frac{1}{3}[/tex]
B. [tex]\frac{1}{9}[/tex]
C. 3
D. 9

Sagot :

GinnyAnswer
To simplify the exponential expression [tex]\(27^{\frac{1}{3}}\)[/tex], we need to understand what this expression represents. The exponent [tex]\(\frac{1}{3}\)[/tex] denotes the cube root of 27.

So, we are looking for a number that, when raised to the power of 3, gives us 27. In other words, we need to solve the following equation:

[tex]\[ x^3 = 27 \][/tex]

The number that satisfies this equation is 3, because:

[tex]\[ 3^3 = 3 \times 3 \times 3 = 27 \][/tex]

Thus, the cube root of 27 is 3. Therefore, the simplified value of [tex]\(27^{\frac{1}{3}}\)[/tex] is:

[tex]\[ \boxed{3} \][/tex]
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