what is the simplified form of (-5a/3)^-3
(-5a/3)^-3 = 1 / ( -5 a / 3 )^3 = 1 / ( -5 a )^3/3^3 = 3^3 / ( -5 a)^3 = 27 / - 125 a^3 = - 27 / 125 a^3
(-5a/3)^-3 = (-3/5a)^3 = -27 / 125a^3
To find the simplified form of the expression (-5a/3)^-3, we can follow the order of operations and the rules of exponents.
Step 1: Manage the Negative Exponent
The negative exponent can be managed by taking the reciprocal of the base raised to the positive exponent.
So, we can rewrite (-5a/3)^-3 as 1/((-5a/3)^3).
Step 2: Simplify the Base
To simplify the base (-5a/3)^3, we raise each term inside the parentheses (numerator and denominator) to the power of 3.
(-5a/3)^3 = (-5^3 * a^3) / (3^3) = -125a^3 / 27
Step 3: Substitute the Simplified Base
Substituting the simplified base into our expression, we get:
1 / (-125a^3 / 27)
Step 4: Simplify the Division
To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the expression as:
1 * (27 / (-125a^3))
Step 5: Simplify Further
Multiplying 1 by 27 gives us:
27 / (-125a^3)
Therefore, the simplified form of (-5a/3)^-3 is 27 / (-125a^3).