Question

simplify: \frac{-15(y^2)^4}{-5y^3 y^2}

• 3y
• -3y^3
• 3y^2
• 3y^3

Explanation:

Simplify the numerator

Using the Evaluating Exponential Expressions knowledge point

$$ (y^2)^4 = y^{2 \times 4} = y^8 $$

The numerator becomes:

$$ -15y^8 $$

Simplify the denominator

Using the Evaluating Exponential Expressions knowledge point

$$ -5y^3 y^2 = -5y^{3+2} = -5y^5 $$

Divide the coefficients

Using the Negative Numbers knowledge point

$$ \frac{-15}{-5} = 3 $$

Divide the variable terms

Using the Evaluating Exponential Expressions knowledge point

$$ \frac{y^8}{y^5} = y^{8-5} = y^3 $$

Combine the results

Using the Evaluating Exponential Expressions and Negative Numbers knowledge points

$$ \frac{-15y^8}{-5y^5} = 3y^3 $$

Answer:

• (A) \(3y\)
• (B) \(-3y^3\)
• (C) \(3y^2\)
• (D) \(3y^3\) (Correct answer)