CheerMath

Grade 8 Exponents & Scientific Notation Practice

Apply Exponent Rules and Build Scientific Notation

Learn the exponent rules! Multiply and divide powers with the same base, raise a power to a power, handle products and quotients, and write both large and small numbers in scientific notation.

Also known as Class 8 maths — the same topics, whether your school calls it grade, class or year.

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Sample questions

A few samples from this topic — try one, then show the answer.

  1. Multiply Powers with the Same Base

    What is the result of 77  ×  747^{7} \; \times \; 7^{4}?
    • 7747^{74}
    • 737^{3}
    • 7117^{11}
    • 7287^{28}
    Show answer
    Answer:
    7117^{11}

  2. Divide Powers with the Same Base

    What goes in the blank? 69  ÷  6□  =  626^{9} \; \div \; 6^{\square} \; = \; 6^{2}
    Show answer
    Answer:
    7

  3. Write Large and Small Numbers in Scientific Notation

    How would you write 19,000 in scientific notation?
    • 19×10319 \times 10^{3}
    • 0.19×1050.19 \times 10^{5}
    • 1.9×1041.9 \times 10^{4}
    • 1.9×1051.9 \times 10^{5}
    Show answer
    Answer:
    1.9×1041.9 \times 10^{4}

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A worked example

What is the result of 77  ×  747^{7} \; \times \; 7^{4}?
  1. We need to simplify 77  ×  747^{7} \; \times \; 7^{4}.
  2. Both powers have the same base (7). The product rule says→\tokeep the base and add the exponents.
  3. 77  ×  74  =  77+4  =  7117^{7} \; \times \; 7^{4} \; = \; 7^{{7+4}} \; = \; 7^{{11}}
  4. The answer is 7117^{{11}}.

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