50 POINTS! Calculate the expression in the most efficient way possible. Show steps. 5^1125 * 0.2^1123

Question

asked Jan 10, 2024 144k views

1 Answer

Webberpuma · Answer 1 · 2024-01-17T09:14:03+0000

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:

$\implies 5 \cdot 5$

$\implies 25$