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Writing Simplify this expression. Assume that y is nonzero. Use pencil and paper. Describe how the values of the expression vary with the values chosen for y. Give examples.
4 y Superscript 0
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Part 1
4 y Superscript 0equals
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Reason: for any nonzero y, y^0 = 1, so 4·y^0 = 4·1 = 4. The value does not change as y changes (as long as y ≠ 0) — it is constant.
Examples:
- y = 2: 4·2^0 = 4·1 = 4
- y = −5: 4·(−5)^0 = 4
- y = 1/10: 4·(1/10)^0 = 4
(If y = 0, 0^0 is indeterminate, which is why the problem assumes y ≠ 0.)
Reason: for any nonzero y, y^0 = 1, so 4·y^0 = 4·1 = 4. The value does not change as y changes (as long as y ≠ 0) — it is constant.
Examples:
- y = 2: 4·2^0 = 4·1 = 4
- y = −5: 4·(−5)^0 = 4
- y = 1/10: 4·(1/10)^0 = 4
(If y = 0, 0^0 is indeterminate, which is why the problem assumes y ≠ 0.)
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