Question

1. $3x^{-7}y^{-8} \cdot 2y$

Explanation:

Step1: Multiply the coefficients

Multiply 3 and 2.
$3\times2 = 6$

Step2: Multiply the x - terms

For the x - term, we have $x^{-7}$ (since there is only one x - term, we just keep it as is for now).

Step3: Multiply the y - terms

Use the rule of exponents $a^m\times a^n=a^{m + n}$. For the y - terms, we have $y^{-8}\times y^{1}=y^{-8 + 1}=y^{-7}=\frac{1}{y^{7}}$ (using the rule $a^{-n}=\frac{1}{a^{n}}$)

Step4: Combine all the terms

Combine the coefficient, x - term, and y - term. So we get $6\times x^{-7}\times\frac{1}{y^{7}}=\frac{6}{x^{7}y^{7}}$

Answer:

$\frac{6}{x^{7}y^{7}}$