Question

1:Rút gọn

a)^{\(\dfrac{15^{30}}{45^{15}}\)}

b)\(\dfrac{2^{15}.9^4}{6^6.8^3}\)

c)\(\dfrac{14^{10}.21^{32}.35^{48}}{10^{10}.15^{32}.7^{96}}\)

2:So sánh

a)3²⁰⁰và 2³⁰⁰

b)9¹² và 26⁸

c)2²⁴ và 3¹⁶

Answer 1

a) \(\dfrac{15^{30}}{45^{15}}=\dfrac{15^{30}}{3^{15}.15^{15}}=\dfrac{15^{15}}{3^{15}}=5^{15}\)

b) \(\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{8^5.3^8}{2^6.3^6.8^3}=\dfrac{8^2.3^2}{2^6}=\dfrac{2^6.3^2}{2^6}=3^2=9\)

c) \(\dfrac{14^{10}.21^{32}.35^{48}}{10^{10}.15^{32}.7^{96}}=\dfrac{2^{10}.7^{10}.3^{32}.7^{32}.5^{48}.7^{48}}{2^{10}.5^{10}.3^{32}.5^{32}.7^{96}}\)

= \(\dfrac{2^{10}.7^{58}.3^{32}.5^{48}}{2^{10}.5^{42}.3^{32}.7^{96}}=\dfrac{5^6}{7^{38}}\) ( Câu này làm bừa, có lẽ sai đấy :)) )

2. So sánh

a) 3²⁰⁰ = 9¹⁰⁰

2³⁰⁰ = 8¹⁰⁰

Vì 9¹⁰⁰ > 8¹⁰⁰ nên 3²⁰⁰ < 2³⁰⁰

b) 9¹² = 729⁴

26⁸ = 676⁴

Vì 729⁴ > 676⁴ nên 9¹² > 26⁸

c) 2²⁴ = 8⁸

3¹⁶ = 9⁸

Vì 8⁸ < 9⁸ nên 2²⁴ < 3¹⁶