Join IDNLearn.com to access a wealth of knowledge and get your questions answered by experts. Ask your questions and get detailed, reliable answers from our community of experienced experts.

Compute: 100 to the power of 999 times 5 to the power of negative 999 times 2 to the power of negative 999.

Sagot :

100 = 10² = 2² × 5², so

100⁹⁹⁹ = (2² × 5²)⁹⁹⁹

100⁹⁹⁹ = 2²ˣ⁹⁹⁹ × 5²ˣ⁹⁹⁹

100⁹⁹⁹ = 2¹⁹⁹⁸ × 5¹⁹⁹⁸

Then

100⁹⁹⁹ × 5⁻⁹⁹⁹ × 2⁻⁹⁹⁹ = 2¹⁹⁹⁸ × 5¹⁹⁹⁸ × 5⁻⁹⁹⁹ × 2⁻⁹⁹⁹

100⁹⁹⁹ × 5⁻⁹⁹⁹ × 2⁻⁹⁹⁹ = 2¹⁹⁹⁸⁻⁹⁹⁹ × 5¹⁹⁹⁸⁻⁹⁹⁹

100⁹⁹⁹ × 5⁻⁹⁹⁹ × 2⁻⁹⁹⁹ = 2⁹⁹⁹ × 5⁹⁹⁹

100⁹⁹⁹ × 5⁻⁹⁹⁹ × 2⁻⁹⁹⁹ = (2 × 5)⁹⁹⁹

100⁹⁹⁹ × 5⁻⁹⁹⁹ × 2⁻⁹⁹⁹ = 10⁹⁹⁹

which is a number with 1000 digits,

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000