Natasha says that $7^{5}$ is bigger than $5^{7}$ . Has Natasha arrived at the right answer?

Yes

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Cannot be determined

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Solution

The correct option is B No
$7^{5} = 7 \times 7 \times 7 \times 7 \times 7 = 16, 807$
[Appying repeated exponentiation]

$5^{7} = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5$ $= 78, 125$

Now,
$∵ 78, 125 > 16, 807$
$\Rightarrow 5^{7} > 7^{5}$
$∴$ Natasha didn't arrive at the right answere,
Hence, option (b) is the correct choice.

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Natasha says that 75 is bigger than 57. Has Natasha arrived at the right answer?

The correct option is B No75=7×7×7×7×7=16,807 [Appying repeated exponentiation] 57=5×5×5×5×5×5×5 =78,125 Now, ∵78,125>16,807 ⇒57>75 ∴ Natasha didn't arrive at the right answere, Hence, option (b) is the correct choice.

Natasha says that $7^{5}$ is bigger than $5^{7}$ . Has Natasha arrived at the right answer?