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Negative Exponents Exploration
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Negative Exponents Exploration
Explore how negative exponents represent repeated division. Show your working for calculation questions.
Understanding the pattern
Each time the exponent decreases by one, divide the value by the base.
1.Which power of 10 has the value 0.01?
- 10⁻¹
- 10⁻²
- 10²
- 10⁻³
2.Select every expression that equals 1/1000.
- 10⁻³
- 0.001
- 1 ÷ 10³
- 10³
3.Evaluate 3⁻².
- −9
- 1/9
- 1/6
- 9
4.Choose the expression equivalent to x⁻⁴, where x is not zero.
- −x⁴
- 1/x⁴
- 4/x
- x/4
Calculate and rewrite
Use the reciprocal rule to work with negative powers.
5.Write 2⁻⁴ as a fraction in simplest form.
6.Calculate 5⁻¹.
7.Evaluate 2⁻⁵. Give your answer as a fraction.
8.Write 1 ÷ 8 ÷ 8 as a single power of 8 with a negative exponent.
9.Express 1/(5 × 5 × 5) as a power of 5 with a negative exponent.
10.Rewrite 1 ÷ 6² using a negative exponent.
11.In one or two sentences, explain what the negative exponent means in 4⁻³.
Using negative exponents
Connect powers to small quantities and scientific notation.
12.A sample is reduced to one tenth of its previous amount each hour. What fraction of its starting amount remains after 4 hours? Write your answer as a power of 10 and as a decimal.
13.Write 0.0007 in scientific notation.
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