Lawson Bond
08/04/2023 · Primary School
(6) Expresa en forma de una sola potencia. \( \begin{array}{lll}\text { a) }\left(33^{2}\right)^{6} & \text { c) }\left(4^{12}\right)^{2} & \text { e) }\left(6^{9}\right)^{4} \\ \text { b) }\left(7^{5}\right)^{3} & \text { d) }(5)^{6} & \text { f) }\left(12^{3}\right)^{0}\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Para expresar cada una de las potencias en forma de una sola potencia, utilizamos la propiedad de las potencias que dice que \((a^m)^n = a^{m \cdot n}\).
Ahora, aplicamos esta propiedad a cada uno de los casos:
a) \((33^{2})^{6} = 33^{2 \cdot 6} = 33^{12}\)
b) \((7^{5})^{3} = 7^{5 \cdot 3} = 7^{15}\)
c) \((4^{12})^{2} = 4^{12 \cdot 2} = 4^{24}\)
d) \((5)^{6} = 5^{6}\) (ya está en forma de una sola potencia)
e) \((6^{9})^{4} = 6^{9 \cdot 4} = 6^{36}\)
f) \((12^{3})^{0} = 12^{3 \cdot 0} = 12^{0} = 1\) (cualquier número elevado a la potencia 0 es 1)
Resumiendo, las expresiones en forma de una sola potencia son:
a) \(33^{12}\)
b) \(7^{15}\)
c) \(4^{24}\)
d) \(5^{6}\)
e) \(6^{36}\)
f) \(1\)
Quick Answer
a) \(33^{12}\)
b) \(7^{15}\)
c) \(4^{24}\)
d) \(5^{6}\)
e) \(6^{36}\)
f) \(1\)
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