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50 POINTS! Calculate the expression in the most efficient way possible. Show steps.

5^1125 * 0.2^1123

User AwfulHack
by
8.3k points

1 Answer

3 votes

Answer:

25

Explanation:

Given expression:


5^(1125) * 0.2^(1123)

Rewrite 0.2 as a fraction:


\implies 5^(1125) * \left((1)/(5)\right)^(1123)


\textsf{Apply exponent rule} \quad \left((a)/(b)\right)^c=(a^c)/(b^c):


\implies 5^(1125) * (1^(1123))/(5^(1123))

Simplify the numerator by applying the exponent rule a¹ = a:


\implies 5^(1125) * (1)/(5^(1123))


\textsf{Apply the fraction rule} \quad a * (b)/(c)=(ab)/(c):


\implies (5^(1125) *1)/(5^(1123))


\implies (5^(1125))/(5^(1123))


\textsf{Apply exponent rule} \quad (a^b)/(a^c)=a^(b-c):


\implies 5^(1125-1123)

Simplify the exponent:


\implies 5^(2)

Simplify:


\implies 5 \cdot 5


\implies 25

User Webberpuma
by
7.8k points