Question

Puneti in evidenta puteri cu aceeasi baza, apoi aplicati regulile de calcul cu puteri pentru a scrie mai simplu :a) 2^15×4^20×8^3 b) 9^3×27^2×3^5 c) (5^10×25^2):5^4 d) (3^4×4^4):12^3

Answer 1

2¹⁵×4²°×8³=2¹⁵x(2²)²°x(2³)³=2¹⁵x2⁴°x2⁹=2¹⁵⁺⁴°⁺⁹=2⁶⁴

9³×27²×3⁵=(3²)³x(3³)²x3⁵=3⁶x3⁶x3⁵=3⁶⁺⁶⁺⁵=3¹⁷

(5¹°×25²):5⁴=[(5¹°x(5²)²]:5⁴=(5¹°x5⁴):5⁴=5¹°⁺⁴⁻⁴=5¹°


(3⁴×4⁴):12³=(3x4)⁴:12³=12⁴:12³=12⁴⁻³=12¹=12

Answer 2

$2^{15} * 4^{20} * 8^{3}= 2^{15}* ( 2^{2}) ^{20}* (2^{3}) ^{3}= 2^{15}* 2^{2*20}* 2^{3*3}= 2^{15}* 2^{40} * 2^{9}=$$2^{15+40+9}= 2^{64}$
$9^{3}* 27^{2} * 3^{5}= (3^{2}) ^{3} * (3^{3})^{2}* 3^{5}= 3^{2*3} * 3^{3*2} * 3^{5}= 3^{6}* 3^{6}* 3^{5} =$$3^{6+6+5}= 3^{17}$
$( 5^{10}* 25^{2}): 5^{4} = ( 5^{10}* (5^{2})^{2}): 5^{4}=( 5^{10}* 5^{4}): 5^{4} = 5^{10+4} : 5^{4} =$$5^{14}: 5^{4}= 5^{14-4}= 5^{10}$
$( 3^{4}* 4^{4} ): 12^{3}= (3*4)^{4} : 12^{3} = 12^{4} : 12^{3}= 12^{4-3}= 12^{1} =12$