simplify:(4xy^2)^-3
To simplify the expression (4xy^2)^-3, we can apply the rule of exponents which states that for any nonzero number a, (a^n)^m is equal to a^(n × m).
Let's break down the expression step by step:
Step 1: Start by applying the exponent to each term inside the parentheses.
(4^-3) * (x^-3) * (y^6)
Step 2: Simplify the values raised to negative exponents.
1/(4^3) * 1/(x^3) * y^6
Step 3: Calculate the values.
1/64 * 1/(x^3) * y^6
Step 4: Combine the terms.
y^6 / (64 * x^3)
So, the simplified form of (4xy^2)^-3 is y^6 / (64 * x^3).
To simplify the expression (4xy^2)^-3, we can use the power of a power rule.
First, we can note that the expression is raised to the power of -3. This means we can rewrite it as the reciprocal of the expression raised to the power of 3.
So, (4xy^2)^-3 can be simplified as (1/(4xy^2)^3).
Now, to simplify further, we can expand the expression inside the parentheses to get rid of the exponent.
(4xy^2)^3 can be expanded as (4^3)(x^3)(y^6), since we multiply the coefficients and raise each variable to the power of 3.
Therefore, (1/(4xy^2)^3) is equal to 1/(64x^3y^6).
So, the simplified form of (4xy^2)^-3 is 1/(64x^3y^6).
Not sure any other version would be simpler, but if you want to get rid of the parentheses,
(4xy^2)^-3
= 1/(4xy^2)^3
= 1 / 64x^3y^6