The value of \(0.1^8 \div 0.01^5\) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 100
Write both decimals as powers of 10; dividing powers of the same base means subtracting the exponents.
\(0.1=10^{-1}\), so \(0.1^{8}=(10^{-1})^{8}=10^{-8}\)
\(0.01=10^{-2}\), so \(0.01^{5}=(10^{-2})^{5}=10^{-10}\)
Dividing, the exponents subtract: \(10^{-8}\div10^{-10}=10^{-8+10}=10^{2}=100\)