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№ 1
Сравнить
80^(13) и
10^(28).

№ $1$ $\newline$ Сравнить $80^{13}$ и $10^{28}$ .

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Evaluate rational exponents

Full solution

Q. №

1

\newline

Сравнить

80^{13}

и

10^{28}

.

Express with common base: First, let's express both numbers with a common base, which is $10$ . We know that $80 = 8 \times 10$ , so we can write $80^{13}$ as $(8\times10)^{13}$ .
Apply power of product rule: Now, let's apply the power of a product rule: $(ab)^c = a^c * b^c$ . So, $(8*10)^{13} = 8^{13} * 10^{13}$ .
Compare with common factor: We can see that $10^{13}$ is a common factor in both $80^{13}$ and $10^{28}$ . So, we can compare $8^{13}$ and $10^{15}$ instead, since $10^{28} = 10^{13} \times 10^{15}$ .
Compare $8^{13}$ and $10^{15}$ : Now, we know that $8 < 10$ , so $8^{13} < 10^{13}$ . Therefore, $8^{13}$ is definitely less than $10^{15}$ .
Conclude $80^{13} < 10^{28}$ : Since $8^{13} < 10^{15}$ , we can conclude that $80^{13}$ is less than $10^{28}$ .

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