Question

Select the equivalent expression. 1/y⁶ =? a.y¹/⁶ b.y ⁻⁶ c.6ʸ

Answer 1

The equivalent expression is:

`b. \( y^(-6) \)`

Step-by-step explanation:

The equivalent expression for
`\( (1)/(y^6) \) is \( y^(-6) \)`, which corresponds to option b. In this expression, the negative exponent indicates the reciprocal of
`\( y^6 \)`, as any non-zero number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent. Therefore,
`\( y^(-6) \)` is the correct equivalent expression.

In mathematical terms,
`\( y^(-6) \) can be understood as \( (1)/(y^6) \).`The negative exponent signifies the inverse or reciprocal of the base raised to the positive exponent. In this case, the base is
`\( y \),` and the positive exponent is 6.

When the exponent is negated, it transforms into its reciprocal, resulting in
`\( y^(-6) \)`. This relationship is fundamental in algebra and is consistent with the rules of exponents. Therefore, option b accurately represents the equivalent expression for
`\( (1)/(y^6) \),`providing a clear and concise solution to the given question.