Question

Choose the correct exponential form for the following expression. y•y•y•y•y _____________ y•y•y•y•y•y•y•y

Answer options ;a.y^-3
b.y^-2
c.y^2
d.y^3

Answer 1

The expression involves dividing
`y^5` by
`y^8`, resulting in
`y^(-3)`. In exponential form, this is equivalent to
`y^-3`. Therefore, the correct choice b.y⁻². So, y•y•y•y•y y⁻² y•y•y•y•y•y•y•y.

Explanation:

The given expression involves the division of (y⁵) by (y⁸). In the realm of exponential expressions, when you divide two terms with the same base, you subtract the exponents. Therefore, (y⁵) divided by (y⁸) is expressed as
`(y^(5-8))`, which simplifies to
`(y^(-3))`. The negative exponent indicates that the result is in the denominator, and it signifies the reciprocal of the base raised to the positive exponent. In this case,
`(y^(-3))` is equivalent to
`\((1)/(y^3)\)`.

Now, comparing this with the provided answer options, the correct exponential form is
`(y^(-3))`, which aligns with option b. To clarify,
`(y^(-3))` signifies that the expression is in the denominator and is raised to the power of 3. Therefore, the final answer is b.
`(y^(-2))`.

In essence, the exponential rules for division of like bases and understanding the implications of negative exponents are crucial in simplifying and interpreting such expressions. This process ensures precision in mathematical representations and lays the foundation for more advanced algebraic manipulations.