Work out the value of 125^(-2/3)

Step 1: Write 125 as an exponent. Is there any number you can multiply by itself a few times to give you 125? The answer is 5 because 5 x 5 x 5= 5 x 25 = 125. Step 2: Since we know that 125=5^3, we can replace 125 in the equation by 5^3; (5^3)^(-2/3). Step 3: Use the power rule (a^b)^c = a^(bc). Applying this rule to our equation we obtain 5^(3-2/3). Step 4: Inside the brackets we have 3*(-2/3). We can break this down further by cancelling out the 3 in the numerator with the 3 in the denominator and we will be left with -2. Step 5: Now we can simplify 5^(3*-2/3) to 5^(-2) Step 6: Apply the negative exponent rule a^(-b)= 1/(a^b)---> 5^(-2) = 1/(5^2) = 1/25