Negative exponents and very small numbers: Class 8 practice
a⁻ⁿ = 1/aⁿ. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Laws of exponents
The idea behind negative exponents and very small numbers
a⁻ⁿ = 1/aⁿ. Very small numbers are written k × 10⁻ⁿ with 1 ≤ k < 10, where n is how many places the point moves to the right.
Step-by-step method
- Rewrite negative powers as reciprocals.
- For small numbers, move the point right past the first non-zero digit.
- The number of places is n in 10⁻ⁿ.
Worked example 1 (Basic)
Find the value of 3^−3.
- = 1/3^3 = 1/27
- Answer: 1/27
Worked example 2 (Standard)
Write 0.000057 in standard form.
- Move the point 5 places right
- = 5.7 × 10^−5
- Answer: 5.7 × 10^−5
Worked example 3 (Challenge)
Write 0.000083 in standard form.
- Move the point 5 places right
- = 8.3 × 10^−5
- Answer: 8.3 × 10^−5
Common mistakes and misconceptions
- Thinking a negative exponent makes the number negative
- Counting zeros instead of places
Practice questions
- (Basic) Find the value of 5^−2.
- (Basic) Find the value of 2^−1.
- (Standard) Write 0.0000024 in standard form.
- (Standard) Write 0.00037 in standard form.
- (Challenge) Write 0.000032 in standard form.
- (Challenge) Write 0.0025 in standard form.
Answer key with full working
- Q1: = 1/5^2 = 1/25 → Answer: 1/25
- Q2: = 1/2^1 = 1/2 → Answer: 1/2
- Q3: Move the point 6 places right → = 2.4 × 10^−6 → Answer: 2.4 × 10^−6
- Q4: Move the point 4 places right → = 3.7 × 10^−4 → Answer: 3.7 × 10^−4
- Q5: Move the point 5 places right → = 3.2 × 10^−5 → Answer: 3.2 × 10^−5
- Q6: Move the point 3 places right → = 2.5 × 10^−3 → Answer: 2.5 × 10^−3
Syllabus note
This skill is listed under "Exponents and Powers" for Class 8 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is negative exponents and very small numbers in?
"Exponents and Powers", Class 8 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.