Question

1. $2x^{-2}y^{3} \cdot 3y^{3}$

Explanation:

Step1: Multiply the coefficients

Multiply the coefficients 2 and 3.
$2\times3 = 6$

Step2: Multiply the variables with the same base (y)

For the variable \( y \), use the rule of exponents \( a^m \cdot a^n = a^{m + n} \). Here, \( y^3 \cdot y^3 = y^{3+3}=y^6 \)

Step3: Combine the results

The \( x \)-term remains as \( x^{-2} \) (since there is no other \( x \)-term to multiply with). Combine the coefficient and the variables.
So, putting it all together, we get \( 6x^{-2}y^6 \). We can also write \( x^{-2} \) as \( \frac{1}{x^2} \), so it can be expressed as \( \frac{6y^6}{x^2} \) (optional, but both forms are correct. If we keep it with negative exponents, it's \( 6x^{-2}y^6 \); if we convert the negative exponent to positive, it's \( \frac{6y^6}{x^2} \))

Answer:

\( 6x^{-2}y^6 \) (or \( \frac{6y^6}{x^2} \))