simplify (make the radicand as small as possible)
125^-2/3
=125^3/2
=square root(125^3)
I'm stuck in this part what do I do next?
please help
125 = 5^3
125^-2/3 = 1/(125^2/3) = 1/(5^3)^2/3 = 1/5^2 = 1/25
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125^3/2 = sqrt(125)^3
not the same thing at all
ok thanx
To simplify the expression 125^(-2/3), you can follow these steps:
1. Rewrite 125^(-2/3) as (125^(1/3))^(-2).
- This step is done by applying the property of raising a power to another power, which states that (a^b)^c = a^(b * c). In this case, a is 125, b is -2/3, and c is 1/3.
2. Evaluate 125^(1/3) to find its cube root.
- The cube root of 125 is 5 because 5^3 = 125.
3. Substitute the value back into the expression.
- (125^(1/3))^(-2) becomes (5)^(-2).
4. Simplify further by applying the power rule for negative exponents.
- The power rule states that a^(-b) = 1/(a^b). In this case, a is 5 and b is 2.
- (5)^(-2) becomes 1/(5^2), which is equal to 1/25.
Therefore, the simplified form of 125^(-2/3) is 1/25.