(sqrt a^3 b^5 c^3)
ab^2c√ac
Can you explain how we do that? Also, the answer key says ab^2 sqrt abc.
the key is correct
a^3 = a^2 * a, so √a^3 = √a^2 * √a = a√a
similarly for b and c
To simplify the expression (sqrt a^3 b^5 c^3), we will use the properties of exponents and apply the rules of square roots.
Let's break it down step by step:
1. First, let's rewrite the expression using fractional exponents:
sqrt(a^3 b^5 c^3) = (a^3/2) * (b^5/2) * (c^3/2)
2. Next, simplify the exponents inside the parentheses:
(a^3/2) = sqrt(a^3) = sqrt(a * a * a) = a * sqrt(a)
(b^5/2) = sqrt(b^5) = sqrt(b * b * b * b * b) = b^2 * sqrt(b)
3. Finally, rewrite the expression with simplified exponents:
(sqrt a^3 b^5 c^3) = a^(3/2) * b^(5/2) * c^(3/2)
Thus, the simplified expression is a^(3/2) * b^(5/2) * c^(3/2).