%5E2%2F3.jpeg "(1/64)^2/3")
Simplifying (1/64)^(2/3)
This article will guide you through simplifying the expression (1/64)^(2/3). We'll break down the steps and explain the concepts involved.
Understanding Fractional Exponents
A fractional exponent like (2/3) represents both a root and a power. The denominator (3) indicates the type of root to take (in this case, a cube root), while the numerator (2) indicates the power to raise the result to.
Step-by-Step Solution
-
Find the cube root of 1/64: The cube root of a number is the value that, when multiplied by itself three times, equals the original number. In this case, the cube root of 1/64 is 1/4 because (1/4) * (1/4) * (1/4) = 1/64.
-
Square the result: Now that we have the cube root of 1/64, which is 1/4, we need to square it. (1/4)² = (1/4) * (1/4) = 1/16.
Therefore, (1/64)^(2/3) simplifies to 1/16.
Key Concepts
- Fractional exponents: Represent both roots and powers.
- Cube root: The value that, when multiplied by itself three times, equals the original number.
By understanding these concepts, you can confidently simplify expressions involving fractional exponents.