To evaluate [tex]\( 64^{2/3} \)[/tex], we can break the problem down into smaller, more manageable steps involving properties of exponents and roots.
1. Rewrite the expression using roots and exponents:
[tex]\[ 64^{2/3} \][/tex]
2. Express 64 as a base raised to an exponent:
[tex]\[ 64 = 4^3 \][/tex]
So,
[tex]\[ 64^{2/3} = (4^{3})^{2/3} \][/tex]
3. Apply exponentiation properties:
Using the property [tex]\((a^m)^n = a^{m \cdot n}\)[/tex],
[tex]\[ (4^{3})^{2/3} = 4^{3 \cdot \frac{2}{3}} \][/tex]
4. Simplify the exponent multiplication:
[tex]\[ 3 \cdot \frac{2}{3} = 2 \][/tex]
5. Evaluate the simplified expression:
[tex]\[ 4^2 = 16 \][/tex]
Therefore,
[tex]\[ 64^{2/3} = 16 \][/tex]
So the final evaluated answer is:
[tex]\[
64^{2/3} = 16
\][/tex]
