Final answer:
To write an equivalent expression for 1/y^-1/4 using positive exponents, we flip the negative exponent to the denominator and simplify the expression.
Step-by-step explanation:
To write an equivalent expression for 1/y^-1/4 using positive exponents, we first need to understand the rule for negative exponents.
The rule states that a negative exponent flips the base and exponent to the denominator, or denotes a division rather than multiplication.
In this case, the negative exponent -1/4 flips the base y^-1/4 to 1/y^1/4.
Now, we need to further simplify the expression by moving the exponent of 1/4 to the numerator, which gives us
=> y^1/4 / y^0.
Finally, any term raised to the power of 0 is equal to 1, so y^0 can be simplified to 1.
Therefore, the equivalent expression for 1/y^-1/4 using positive exponents is y^1/4.