The expression given is the key to saving a planet from being hit by an asteroid. Missy has to find the number that will not completely divide
$(7^{22} + 7^{23} + 7^{24} + 7^{25} + 7^{26})$ .

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Solution

The correct option is D 17
Given:

$(7^{22} + 7^{23} + 7^{24} + 7^{25} + 7^{26})$

$Take 7^{22} common. We get:$

$⟹ (7^{22} \times (7 + 7^{2} + 7^{3} + 7^{4}))$

$⟹ (7^{22} \times (1 + 7 + 7^{2} + 7^{3}))$

$⟹ (7^{22} \times (1 + 7 + 49 + 343))$

$⟹ (7^{22} \times (1 + 7 + 49 + 343))$

$⟹ (7^{22} \times 400)$

$⟹ (7^{22} \times 8 \times 5 \times 10)$

$∴ (7^{22} \times 8 \times 5 \times 10)$ will be divisble by 8, 5, and 10 but not 17.

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The expression given is the key to saving a planet from being hit by an asteroid. Missy has to find the number that will not completely divide (722+723+724+725+726).

The correct option is D 17Given: (722+723+724+725+726) Take 722 common. We get: ⟹(722×(7+72+73+74)) ⟹(722×(1+7+72+73)) ⟹(722×(1+7+49+343)) ⟹(722×(1+7+49+343)) ⟹(722×400) ⟹(722×8×5×10) ∴(722×8×5×10) will be divisble by 8, 5, and 10 but not 17.

The expression given is the key to saving a planet from being hit by an asteroid. Missy has to find the number that will not completely divide
$(7^{22} + 7^{23} + 7^{24} + 7^{25} + 7^{26})$ .