Answer :
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]
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]
