(a^2 b^3)^2
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(a^4 b^2 c)^2
Is Simplified answer b^2
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a^4 c^2
To simplify the expression (a^2 b^3)^2 / (a^4 b^2 c)^2, we can apply the rules of exponents and simplify each term separately before dividing.
First, let's simplify the numerator (a^2 b^3)^2:
To raise a power to a power, we multiply the exponents, so (a^2 b^3)^2 becomes a^(2*2) * b^(3*2) = a^4 * b^6.
Next, let's simplify the denominator (a^4 b^2 c)^2:
Applying the same rule, (a^4 b^2 c)^2 becomes a^(4*2) * b^(2*2) * c^2 = a^8 * b^4 * c^2.
Now we can substitute the simplified values back into the original expression:
(a^2 b^3)^2 / (a^4 b^2 c)^2 simplifies to:
(a^4 * b^6) / (a^8 * b^4 * c^2).
To divide the terms with the same base, we subtract the exponents:
(a^4 * b^6) / (a^8 * b^4 * c^2) = a^(4-8) * b^(6-4) * c^(-2) = a^(-4) * b^2 * c^(-2).
Finally, since any number or variable raised to the power -n can be written as 1 / (number or variable)^n, we can rewrite the expression with positive exponents:
a^(-4) * b^2 * c^(-2) = 1 / (a^4) * b^2 * 1 / (c^2).
Therefore, the simplified answer is:
b^2 / (a^4 * c^2).