Evaluate 8^(-2/3)

Problem

8(−2/3)

Solution

1. Apply the negative exponent rule by rewriting the expression as a reciprocal with a positive exponent.

8(−2/3)=1/(8(2/3))

2. Rewrite the rational exponent using the property a(m/n)=(√(n,a))m to separate the root and the power.

1/(8(2/3))=1/((√(3,8))2)

3. Evaluate the cube root of the base number.

√(3,8)=2

4. Substitute the root back into the expression and square the result.

1/2=1/4

Final Answer

8(−2/3)=1/4

Want more problems? Check here!