Asked by D4VD

Ramesh examined the pattern in the table.

Powers of 7
Value
7 Superscript 4
2,401
7 Superscript 3
343
7 Superscript 2
49
7 Superscript 1
7
7 Superscript 0
1
7 Superscript negative 1
StartFraction 1 Over 7 EndFraction

Ramesh says that based on the pattern 7 Superscript negative 5 = negative 16,807. Which statement explains whether Ramesh is correct?
Ramesh is correct because 7 Superscript negative 5 is equivalent to Negative 7 times (negative 7) times (negative 7) times (negative 7) times (negative 7), which has the same value as Negative 16,807.
Ramesh is correct because as the exponents decrease, the previous value is divided by 7, so 7 Superscript negative 5 = 1 divided by 7 divided by 7 divided by 7 divided by 7 divided by 7 = negative 16,807.
Ramesh is not correct because 7 Superscript negative 5 is equivalent to StartFraction 1 Over 7 Superscript 5 EndFraction, which has the same value as StartFraction 1 Over 7 Superscript 4 EndFraction divided by 7 = StartFraction 1 Over 7 cubed EndFraction = StartFraction 1 Over 343 EndFraction.
Ramesh is not correct because as the exponents decrease, the previous value is divided by 7, so 7 Superscript negative 5 = 1 divided by 7 divided by 7 divided by 7 divided by 7 divided by 7 = StartFraction 1 Over 16,807 EndFraction.

All Answers 1

Answered by GPT-5 mini AI
The fourth statement is correct.

Reason: 7^(−5) = 1 / 7^5 = 1 / 16,807. A negative exponent gives the reciprocal, not a negative number, so Ramesh is incorrect.