If 2*5=9 and 4**0=16 and 8**3=67, and 3**8=17, what is the value of 8**8? (A) 64 (B) 65 (C) 66 (D) 72 (E) 68

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Analyze Pattern in Rules: We need to understand the pattern in the given operation rules. Let's analyze the first rule: 2**5 = 9 This does not follow the standard exponentiation rules, so there must be a different operation being applied here. We need to find a pattern that applies to all the given rules.Examine Rule 1: Let's look at the second rule: 4**0 = 16 Again, this does not follow the standard rules of exponentiation, as 4 to the power of 0 should be 1. We need to continue looking for a pattern.Examine Rule 2: Now, let's examine the third rule: 8**3 = 67 Standard exponentiation would give us 512, not 67. We need to find the relationship between the base, the exponent, and the result.Examine Rule 3: Let's analyze the fourth rule: 3**8 = 17 This also does not follow the standard rules of exponentiation, as 3 to the power of 8 should be 6561. We need to find the pattern that connects the base and exponent to the result.Examine Rule 4: By examining the given rules, we can see that the operation defined by ＂**＂ does not correspond to exponentiation. Instead, it seems that the operation takes the base and adds it to the exponent to get the result. Let's test this hypothesis: For 2**5, the base is 2 and the exponent is 5. Adding them gives us 2 + 5 = 7, but the result given is 9, which is 2 more than 7. For 4**0, the base is 4 and the exponent is 0. Adding them gives us 4 + 0 = 4, but the result given is 16, which is 12 more than 4. For 8**3, the base is 8 and the exponent is 3. Adding them gives us 8 + 3 = 11, but the result given is 67, which is 56 more than 11. For 3**8, the base is 3 and the exponent is 8. Adding them gives us 3 + 8 = 11, but the result given is 17, which is 6 more than 11. It seems that the pattern is not simply adding the base and the exponent. We need to find a consistent operation that applies to all given rules.Test Hypothesis 1: Upon closer inspection, we can see that the result is always one more than the product of the base and the exponent. Let's test this hypothesis: For 2**5, the base is 2 and the exponent is 5. Multiplying them gives us 2 * 5 = 10, and adding 1 gives us 11, but the result given is 9. This does not match our hypothesis.

If $2 \times 5=9$ and $4 \times 0=16$ and $8 \times 3=67$ , and $3 \times 8=17$ , what is the value of $8 \times 8 ?$ $\newline$ (A) $64$ $\newline$ (B) $65$ $\newline$ (C) $66$ $\newline$ (D) $72$ $\newline$ (E) $68$

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If 2×5=9 2 \times 5=9 2×5=9 and 4×0=16 4 \times 0=16 4×0=16 and 8×3=67 8 \times 3=67 8×3=67, and 3×8=17 3 \times 8=17 3×8=17, what is the value of 8×8? 8 \times 8 ? 8×8?\newline(A) 646464\newline(B) 656565\newline(C) 666666\newline(D) 727272\newline(E) 686868

If $2 \times 5=9$ and $4 \times 0=16$ and $8 \times 3=67$ , and $3 \times 8=17$ , what is the value of $8 \times 8 ?$ $\newline$ (A) $64$ $\newline$ (B) $65$ $\newline$ (C) $66$ $\newline$ (D) $72$ $\newline$ (E) $68$