write 3^-2/3 as a single of 3
To write 3^-2/3 as a single power of 3, you can rearrange the expression using the rules of exponentiation.
Step 1: Start with the expression 3^-2/3.
Step 2: Apply the power rule, which states that when you have a negative exponent, you can move it to the denominator as a positive exponent. In this case, we move the -2 to the denominator:
3^-2/3 = 1 / 3^2/3
Step 3: Simplify the exponent 2/3. The fractional exponent represents the cube root of the base raised to the power of the numerator. Cube root is the opposite of cubing, so we want to find what number cubed equals 3. In this case, the cube root of 3 is ∛3.
Therefore, 3^-2/3 can be written as 1 / ∛3^2.
Step 4: Simplify ∛3^2. Raising ∛3 to the power of 2 means cubing it and then squaring the result:
∛3^2 = (∛3)^2 = (3)^(2/3)
So the final expression is 1 / (3)^(2/3).