Cube of 7: How to Calculate 7³ and Why It Equals 343

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The cube of 7 is 343: 7³ = 7 × 7 × 7 = 343. The small 3 means to use 7 as a factor three times; it does not mean 7 × 3.

How to calculate 7 cubed

1. Write the number in exponent notation: 7³.

2. Expand the exponent into three factors of 7: 7 × 7 × 7.

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3. Multiply the first two factors: 7 × 7 = 49.

4. Multiply by the remaining factor: 49 × 7 = 343.

Therefore, 7³ = 343. The Papua New Guinea Department of Education’s Grade 7 mathematics lesson on cubes and cube roots identifies 7 as the base and 3 as the exponent in this notation.

What does “cubed” mean?

“Seven cubed” and “seven raised to the third power” are two ways to say 7³. The base is 7, and the exponent is 3. The exponent tells you how many times the base appears as a factor, so 7³ means 7 × 7 × 7—not 7 × 3.

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Picture 7³ as a cube

A cube with sides 7 units long can be pictured as seven layers of unit blocks. Each layer has 7 × 7 = 49 blocks; seven such layers contain 7 × 49 = 343 blocks. This connects the three factors in 7 × 7 × 7 to the cube’s three equal dimensions. The University of Waterloo’s exponents lesson also connects cubed numbers with the volume of a cube. A physical model is optional—the multiplication alone gives the answer.

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