Inicio › Matemáticas 1 › Reglas de exponentes

Matemáticas 1 · Tema 10

Reglas de exponentes

Leyes, base 10 y radicales

Formulario

  • Producto $a^n \cdot a^m = a^{n+m}$
  • Cociente $\dfrac{a^n}{a^m} = a^{n-m}$
  • Pot. de pot. $(a^n)^m = a^{n \cdot m}$
  • Exp. cero $a^0 = 1$
  • Exp. negativo $a^{-n} = \dfrac{1}{a^n}$
  • Exp. fraccionario $a^{n/m} = \sqrt[m]{a^n}$

Ejemplos

  • $\dfrac{10^2}{10^8} = 10^{2-8} = 10^{-6} = $ $0.000001$
  • $10^4 \cdot 10^3 = 10^{4+3} = 10^7 = $ $10{,}000{,}000$
  • $10^{-4} = \dfrac{1}{10^4} = \dfrac{1}{10{,}000} = $ $0.0001$
  • $10^3 (10^{-2}) = 10^{3-2} = 10^1 = $ $10$
  • $10^5 = $ $100{,}000$
  • $35^0 = $ $1$
  • $(-1)^5 = $ $-1$
  • $5^{-4} = \dfrac{1}{5^4} = $ $\dfrac{1}{625}$
  • $(5^2)^3 = 5^{2 \cdot 3} = $ $5^6$
  • $(2)^4 (2)^3 = 2^{4+3} = $ $2^7$
  • $\dfrac{3^4}{3^6} = 3^{4-6} = 3^{-2} = $ $\dfrac{1}{3^2}$
  • $(7)^{5/3} = $ $\sqrt[3]{7^5}$

Ejercicios

Aplica las reglas para simplificar cada expresión.

  • $\dfrac{10^4}{10^6} = $
  • $10^2 (10)^{-4} = $
  • $10^{-4} (10^7) = $
  • $10^{-4} = $
  • $10^{-4} / 10^7 = $
  • $\dfrac{10^6}{10^1} = $
  • $(10^3)(10)^2 = $
  • $10^{+3} = $
  • $(10^5)(10^{-4}) = $
  • $10^5 = $
  • $\dfrac{10^{10}}{10^3} = $
  • $10^{-7} (10^{21}) = $
  • $10^6 (10)^2 = $
  • $10^7 = $
  • $10^2 / 10^5 = $
  • $72^0 = $
  • $(-1)^7 = $
  • $(3)^2 (3)^4 = $
  • $\dfrac{2^4}{2} = $
  • $\dfrac{(3)^4}{(5)^4} = $
  • $(-1)^4 = $
  • $4^{-3} = $
  • $(7)^{1/3} = $
  • $\dfrac{(-3)^5}{(-3)^8} = $
  • $2^{3/5} = $
  • $43^0 = $
  • $(-1)^6 = $
  • $(4)^5 (4)^2 = $
  • $\dfrac{3^4}{3^2} = $
  • $\dfrac{5^3}{6^3} = $
  • $8^{4/7} = $
  • $(2^3)^4 = $

Respuestas

▼
  • $\dfrac{10^4}{10^6} = 10^{-2} = $ $0.01$
  • $10^2 (10)^{-4} = 10^{-2} = $ $0.01$
  • $10^{-4} (10^7) = 10^3 = $ $1{,}000$
  • $10^{-4} = $ $0.0001$
  • $10^{-4} / 10^7 = $ $10^{-11}$
  • $\dfrac{10^6}{10^1} = 10^5 = $ $100{,}000$
  • $(10^3)(10)^2 = 10^5 = $ $100{,}000$
  • $10^{+3} = $ $1{,}000$
  • $(10^5)(10^{-4}) = 10^1 = $ $10$
  • $10^5 = $ $100{,}000$
  • $\dfrac{10^{10}}{10^3} = 10^7 = $ $10{,}000{,}000$
  • $10^{-7} (10^{21}) = $ $10^{14}$
  • $10^6 (10)^2 = $ $10^8$
  • $10^7 = $ $10{,}000{,}000$
  • $10^2 / 10^5 = 10^{-3} = $ $0.001$
  • $72^0 = $ $1$
  • $(-1)^7 = $ $-1$
  • $(3)^2 (3)^4 = 3^6 = $ $729$
  • $\dfrac{2^4}{2} = 2^3 = $ $8$
  • $\dfrac{(3)^4}{(5)^4} = \left(\dfrac{3}{5}\right)^4 = $ $\dfrac{81}{625}$
  • $(-1)^4 = $ $1$
  • $4^{-3} = \dfrac{1}{4^3} = $ $\dfrac{1}{64}$
  • $(7)^{1/3} = $ $\sqrt[3]{7}$
  • $\dfrac{(-3)^5}{(-3)^8} = (-3)^{-3} = $ $-\dfrac{1}{27}$
  • $2^{3/5} = $ $\sqrt[5]{2^3}$
  • $43^0 = $ $1$
  • $(-1)^6 = $ $1$
  • $(4)^5 (4)^2 = 4^7 = $ $16{,}384$
  • $\dfrac{3^4}{3^2} = 3^2 = $ $9$
  • $\dfrac{5^3}{6^3} = $ $\dfrac{125}{216}$
  • $8^{4/7} = $ $\sqrt[7]{8^4}$
  • $(2^3)^4 = 2^{12} = $ $4{,}096$

Ejercicios extra

▼
  • $\dfrac{10^8}{10^{12}} = $
  • $10^{-3} (10)^{-2} = $
  • $10^{0} \cdot 10^{5} = $
  • $(10^2)^{-3} = $
  • $10^9 / 10^{-2} = $
  • $10^{-5} = $
  • $10^6 \cdot 10^{-6} = $
  • $\dfrac{10^{-2}}{10^{-4}} = $
  • $(10^{-1})^{5} = $
  • $10^3 \cdot 10^{-5} \cdot 10^{2} = $
  • $\dfrac{10^7 \cdot 10^{-3}}{10^4} = $
  • $(10^{-2})^{-4} = $
  • $10^{-6} / 10^{-2} = $
  • $10^1 \cdot 10^1 = $
  • $150^0 = $
  • $(-1)^{100} = $
  • $(-2)^3 = $
  • $(1/2)^{-2} = $
  • $(x^2)^5 = $
  • $\sqrt[4]{16} = $
  • $3^{2/3} = $
  • $\sqrt{25^3} = $
  • $(2/3)^3 = $
  • $a^n \cdot a^0 = $
  • $(4^2)^0 = $
  • $(-3)^4 = $
  • $\dfrac{x^5}{x^2} = $
  • $9^{1/2} = $
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