Inicio › Matemáticas 1 › Reglas de exponentes

Matemáticas 1 · Tema 10

Reglas de exponentes

Leyes, base 10 y radicales

Formulario

  • Producto an⋅am=an+ma^n \cdot a^m = a^{n+m}
  • Cociente anam=an−m\dfrac{a^n}{a^m} = a^{n-m}
  • Pot. de pot. (an)m=an⋅m(a^n)^m = a^{n \cdot m}
  • Exp. cero a0=1a^0 = 1
  • Exp. negativo a−n=1ana^{-n} = \dfrac{1}{a^n}
  • Exp. fraccionario an/m=anma^{n/m} = \sqrt[m]{a^n}

Ejemplos

  • 102108=102−8=10−6=\dfrac{10^2}{10^8} = 10^{2-8} = 10^{-6} = 0.0000010.000001
  • 104⋅103=104+3=107=10^4 \cdot 10^3 = 10^{4+3} = 10^7 = 10,000,00010{,}000{,}000
  • 10−4=1104=110,000=10^{-4} = \dfrac{1}{10^4} = \dfrac{1}{10{,}000} = 0.00010.0001
  • 103(10−2)=103−2=101=10^3 (10^{-2}) = 10^{3-2} = 10^1 = 1010
  • 105=10^5 = 100,000100{,}000
  • 350=35^0 = 11
  • (−1)5=(-1)^5 = −1-1
  • 5−4=154=5^{-4} = \dfrac{1}{5^4} = 1625\dfrac{1}{625}
  • (52)3=52⋅3=(5^2)^3 = 5^{2 \cdot 3} = 565^6
  • (2)4(2)3=24+3=(2)^4 (2)^3 = 2^{4+3} = 272^7
  • 3436=34−6=3−2=\dfrac{3^4}{3^6} = 3^{4-6} = 3^{-2} = 132\dfrac{1}{3^2}
  • (7)5/3=(7)^{5/3} = 753\sqrt[3]{7^5}

Ejercicios

Aplica las reglas para simplificar cada expresión.

  • 104106=\dfrac{10^4}{10^6} =
  • 102(10)−4=10^2 (10)^{-4} =
  • 10−4(107)=10^{-4} (10^7) =
  • 10−4=10^{-4} =
  • 10−4/107=10^{-4} / 10^7 =
  • 106101=\dfrac{10^6}{10^1} =
  • (103)(10)2=(10^3)(10)^2 =
  • 10+3=10^{+3} =
  • (105)(10−4)=(10^5)(10^{-4}) =
  • 105=10^5 =
  • 1010103=\dfrac{10^{10}}{10^3} =
  • 10−7(1021)=10^{-7} (10^{21}) =
  • 106(10)2=10^6 (10)^2 =
  • 107=10^7 =
  • 102/105=10^2 / 10^5 =
  • 720=72^0 =
  • (−1)7=(-1)^7 =
  • (3)2(3)4=(3)^2 (3)^4 =
  • 242=\dfrac{2^4}{2} =
  • (3)4(5)4=\dfrac{(3)^4}{(5)^4} =
  • (−1)4=(-1)^4 =
  • 4−3=4^{-3} =
  • (7)1/3=(7)^{1/3} =
  • (−3)5(−3)8=\dfrac{(-3)^5}{(-3)^8} =
  • 23/5=2^{3/5} =
  • 430=43^0 =
  • (−1)6=(-1)^6 =
  • (4)5(4)2=(4)^5 (4)^2 =
  • 3432=\dfrac{3^4}{3^2} =
  • 5363=\dfrac{5^3}{6^3} =
  • 84/7=8^{4/7} =
  • (23)4=(2^3)^4 =

Respuestas

▼
  • 104106=10−2=\dfrac{10^4}{10^6} = 10^{-2} = 0.010.01
  • 102(10)−4=10−2=10^2 (10)^{-4} = 10^{-2} = 0.010.01
  • 10−4(107)=103=10^{-4} (10^7) = 10^3 = 1,0001{,}000
  • 10−4=10^{-4} = 0.00010.0001
  • 10−4/107=10^{-4} / 10^7 = 10−1110^{-11}
  • 106101=105=\dfrac{10^6}{10^1} = 10^5 = 100,000100{,}000
  • (103)(10)2=105=(10^3)(10)^2 = 10^5 = 100,000100{,}000
  • 10+3=10^{+3} = 1,0001{,}000
  • (105)(10−4)=101=(10^5)(10^{-4}) = 10^1 = 1010
  • 105=10^5 = 100,000100{,}000
  • 1010103=107=\dfrac{10^{10}}{10^3} = 10^7 = 10,000,00010{,}000{,}000
  • 10−7(1021)=10^{-7} (10^{21}) = 101410^{14}
  • 106(10)2=10^6 (10)^2 = 10810^8
  • 107=10^7 = 10,000,00010{,}000{,}000
  • 102/105=10−3=10^2 / 10^5 = 10^{-3} = 0.0010.001
  • 720=72^0 = 11
  • (−1)7=(-1)^7 = −1-1
  • (3)2(3)4=36=(3)^2 (3)^4 = 3^6 = 729729
  • 242=23=\dfrac{2^4}{2} = 2^3 = 88
  • (3)4(5)4=(35)4=\dfrac{(3)^4}{(5)^4} = \left(\dfrac{3}{5}\right)^4 = 81625\dfrac{81}{625}
  • (−1)4=(-1)^4 = 11
  • 4−3=143=4^{-3} = \dfrac{1}{4^3} = 164\dfrac{1}{64}
  • (7)1/3=(7)^{1/3} = 73\sqrt[3]{7}
  • (−3)5(−3)8=(−3)−3=\dfrac{(-3)^5}{(-3)^8} = (-3)^{-3} = −127-\dfrac{1}{27}
  • 23/5=2^{3/5} = 235\sqrt[5]{2^3}
  • 430=43^0 = 11
  • (−1)6=(-1)^6 = 11
  • (4)5(4)2=47=(4)^5 (4)^2 = 4^7 = 16,38416{,}384
  • 3432=32=\dfrac{3^4}{3^2} = 3^2 = 99
  • 5363=\dfrac{5^3}{6^3} = 125216\dfrac{125}{216}
  • 84/7=8^{4/7} = 847\sqrt[7]{8^4}
  • (23)4=212=(2^3)^4 = 2^{12} = 4,0964{,}096

Ejercicios extra

▼
  • 1081012=\dfrac{10^8}{10^{12}} =
  • 10−3(10)−2=10^{-3} (10)^{-2} =
  • 100⋅105=10^{0} \cdot 10^{5} =
  • (102)−3=(10^2)^{-3} =
  • 109/10−2=10^9 / 10^{-2} =
  • 10−5=10^{-5} =
  • 106⋅10−6=10^6 \cdot 10^{-6} =
  • 10−210−4=\dfrac{10^{-2}}{10^{-4}} =
  • (10−1)5=(10^{-1})^{5} =
  • 103⋅10−5⋅102=10^3 \cdot 10^{-5} \cdot 10^{2} =
  • 107⋅10−3104=\dfrac{10^7 \cdot 10^{-3}}{10^4} =
  • (10−2)−4=(10^{-2})^{-4} =
  • 10−6/10−2=10^{-6} / 10^{-2} =
  • 101⋅101=10^1 \cdot 10^1 =
  • 1500=150^0 =
  • (−1)100=(-1)^{100} =
  • (−2)3=(-2)^3 =
  • (1/2)−2=(1/2)^{-2} =
  • (x2)5=(x^2)^5 =
  • 164=\sqrt[4]{16} =
  • 32/3=3^{2/3} =
  • 253=\sqrt{25^3} =
  • (2/3)3=(2/3)^3 =
  • an⋅a0=a^n \cdot a^0 =
  • (42)0=(4^2)^0 =
  • (−3)4=(-3)^4 =
  • x5x2=\dfrac{x^5}{x^2} =
  • 91/2=9^{1/2} =
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