Year 9 Maths • AC9M9A01 • Authored homework
Index laws, negative exponents and SI prefixes
Use index laws with positive and negative integer exponents, scientific notation and SI prefixes to simplify expressions and interpret very large or very small quantities. Show working, use correct notation and check reasonableness.
Part A
Short-answer questions
Simplify 3^4 × 3^2.
Simplify a^7 ÷ a^3, where a ≠ 0.
Simplify (x^2)^5.
Write 10^-3 as a fraction and name the SI prefix connected to 10^-3.
Convert 4.5 km to metres.
Convert 3200 mg to grams.
Write 0.000006 in scientific notation.
Explain why 5^0 = 1.
Correct this error: 2^-3 = -8.
Give one real-world context where negative exponents or SI prefixes are useful.
Part B
Long-answer questions
Simplify (2x^3y^-2)(4x^-1y^5) and write the answer with positive exponents.
A sensor records 0.0000048 m. Write this distance in scientific notation and in micrometres.
Compare 3.2 × 10^5 and 4.7 × 10^4. Explain which is larger and by what factor approximately.
A student writes (a^3)^2 = a^5. Explain the mistake and correct it using the index law.
Convert 7.5 gigabytes to bytes using powers of 10, then explain the meaning of the prefix giga.
Use index laws to simplify a multi-step expression containing multiplication, division and a power of a power.
Explain how SI prefixes help scientists and engineers avoid very long decimals or very large numbers.
A medicine dose is measured in micrograms but a scale reads milligrams. Create and solve a conversion problem.
Write a full worked solution involving scientific notation, SI prefixes and index laws, including unit checks.
Create a table of five SI prefixes from kilo to micro, showing the power of 10 and an example measurement.
Part C
Research and understanding task
Research one SI prefix used in science, computing, medicine or engineering. Explain its power of 10, give three examples, and create a conversion problem using it.