Question

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

5^1125 * 0.2^1123

Answer 1

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`