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Exponents and scientific notation test

Repeated multiplication, the rules that shortcut it, and the notation that puts it to work.

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Exponents and scientific notation test
Exponents and scientific notation test — printable test paper

The answer key prints on a separate page.

What's on this test

An exponent is a count of factors, and almost every exponent error is that count getting handled like the number it sits on. x² · x³ is five x's multiplied, so the exponents add to five — the confident wrong answer is x⁶, multiplying the twos and threes because that is what the base is asking for. Section 1 tests the meaning; the power rules in section 2 are only worth memorizing once that meaning is what they are shorthand for.

How the paper is put together

Scientific notation is the same idea aimed at size rather than algebra: a number written as a digit-and-a-bit times a power of ten. Expanding 4.2 × 10³ into 4,200 checks that the exponent is understood as places moved, not zeros written, and operating in scientific notation is where a shaky power rule finally shows — multiplying the fronts is easy, and it is the exponents that decide whether the answer is off by a factor of a thousand.

The sections on this paper

  1. Exponents6 questions
  2. Laws of exponents5 questions
  3. Scientific notation5 questions
  4. Multiplying and dividing in scientific notation5 questions

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