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Factoring - Comparing Factored Numbers - 3 Factors (Level 3)

This math topic focuses on factoring and comparing factored numbers involving three factors. Students practice applying the correct comparison operators (less than, greater than, or equal to) between different sets of expressions. These expressions involve exponential notations with bases of integers being raised to various powers. Each problem requires selecting whether one factored number is less than, greater than, or equal to another, helping develop skills in exponent manipulation, multiplication, and comparative reasoning. This is part of a broader lesson that includes practice in factoring, multiplication, division, and fractions.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Comparing Factored Numbers - 3 Factors

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Choose the correct comparison operator

312⋅29    ◯    311⋅29⋅51<,>,or=?3^{12}\cdot2^{9}\;\; \bigcirc \;\;3^{11}\cdot2^{9}\cdot5^{1}\\<, >, or = ?

Factoring - Comparing Factored Numbers - 3 Factors Worksheet

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Math worksheet on 'Factoring - Comparing Factored Numbers - 3 Factors (Level 3)'. Part of a broader unit on 'Factoring, Multiplication, Division, Fractions - Practice' Learn online: app.mobius.academy/math/units/factoring_multiplication_division_fractions_practice/
1
Choose the correct comparison operator
A LaTex expression showing 2 to the power of 11 times 5 to the power of 9 times 3 to the power of 1 \;\; \bigcirc \;\;2 to the power of 11 times 5 to the power of 9 times 3 to the power of 1 \\<, >, or = ?
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2
Choose the correct comparison operator
A LaTex expression showing 3 to the power of 9 times 2 to the power of 10 times 7 to the power of 2 \;\; \bigcirc \;\;3 to the power of 10 times 2 to the power of 11 \\<, >, or = ?
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3
Choose the correct comparison operator
A LaTex expression showing 2 to the power of 10 times 7 to the power of 11 \;\; \bigcirc \;\;2 to the power of 10 times 7 to the power of 11 \\<, >, or = ?
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4
Choose the correct comparison operator
A LaTex expression showing 5 to the power of 9 times 7 to the power of 9 times 2 to the power of 11 \;\; \bigcirc \;\;5 to the power of 9 times 7 to the power of 9 times 2 to the power of 11 \\<, >, or = ?
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5
Choose the correct comparison operator
A LaTex expression showing 7 to the power of 9 times 3 to the power of 12 \;\; \bigcirc \;\;7 to the power of 10 times 3 to the power of 10 times 5 to the power of 1 \\<, >, or = ?
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6
Choose the correct comparison operator
A LaTex expression showing 7 to the power of 10 times 2 to the power of 11 \;\; \bigcirc \;\;7 to the power of 9 times 2 to the power of 10 times 3 to the power of 1 times 5 to the power of 1 \\<, >, or = ?
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<
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7
Choose the correct comparison operator
A LaTex expression showing 3 to the power of 10 times 7 to the power of 9 times 5 to the power of 10 \;\; \bigcirc \;\;3 to the power of 9 times 7 to the power of 9 times 5 to the power of 9 times 2 to the power of 2 \\<, >, or = ?
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=