Question

simplify the following expression.

\\(\frac{12a^3b^6c^5}{3a^2b^4c^5}\\)

\\(\bigcirc\\) \\(4ab^2\\)
\\(\bigcirc\\) \\(9ab^2\\)
\\(\bigcirc\\) \\(9ab^2c\\)
\\(\bigcirc\\) \\(4ab^2c\\)

Explanation:

⚡ Using what you learned: properties of exponents

Step 1: Divide the coefficients

$$ \frac{12}{3} = 4 $$

Step 2: Simplify the variable \(a\)

$$ \frac{a^3}{a^2} = a^{3-2} = a^1 = a $$

Step 3: Simplify the variable \(b\)

$$ \frac{b^6}{b^4} = b^{6-4} = b^2 $$

Step 4: Simplify the variable \(c\)

$$ \frac{c^5}{c^5} = c^{5-5} = c^0 = 1 $$

Step 5: Combine the terms

$$ 4 \cdot a \cdot b^2 \cdot 1 = 4ab^2 $$

Answer:

\(4ab^2\)