Questions: Знайдіть значення виразу y^(-8):(y^3)^(-2), якщо y=-2.

Find the value of the expression $y^{-8}:\left(y^{3}\right)^{-2}$, where $y=-2$.

Simplify the exponent in the second term

$\left(y^{3}\right)^{-2} = y^{3 \cdot (-2)} = y^{-6}$

Rewrite the expression using the simplified exponent

$y^{-8}:\left(y^{3}\right)^{-2} = y^{-8} : y^{-6}$

Apply the division rule for exponents

When dividing powers with the same base, we subtract the exponents: $y^{-8} : y^{-6} = y^{-8-(-6)} = y^{-8+6} = y^{-2}$

Substitute $y = -2$ into the expression

$y^{-2} = (-2)^{-2} = \frac{1}{(-2)^2} = \frac{1}{4}$

The value of the expression is $\boxed{\frac{1}{4}}$

The value of the expression $y^{-8}:\left(y^{3}\right)^{-2}$ when $y=-2$ is $\boxed{\frac{1}{4}}$, which corresponds to answer B.