Given that $y^{1/8} imes y^{eta} = y^{k}$, find the value of $k$. - OCR - GCSE Maths - Question 2 - 2018 - Paper 1

To solve the equation y^{1/8} imes y^{eta} = y^{k}, we can use the property of exponents that states when multiplying like bases, we add the exponents:

y^{1/8 + eta} = y^{k}

This implies that the exponents must be equal:

1/8 + eta = k

To find $k$, we need to express $k$ in terms of $1/8$ and eta. Since eta is not provided, we assume it to be 0 for simplicity, yielding:

$k = 1/8 + 0 = 1/8$

Assuming $y$ cannot be zero, we conclude:

If any additional context was given regarding the value of eta, adjust accordingly, but under standard conditions:

Thus, in the absence of additional information, one typical solution is:

k = rac{1}{8}