2 to the Power of 3
Instantly calculate 2 raised to the 3rd power with step-by-step logic.
Step-by-Step Breakdown
= 8
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Understanding 2 to the Power of 3
What does 23 mean?
When you see the mathematical expression 2 to the power of 3 (written as 23), it means you are taking the base number (2) and multiplying it by itself three times. The small number at the top right is called the exponent or power.
$$2^3 = \underbrace{2 \times 2 \times 2}_{3 \text{ times}} = 8$$Because the exponent is a 3, this specific operation is commonly referred to as “2 cubed”.
Why is it called “2 Cubed”?
The term “cubed” comes from 3D geometry! If you have a physical cube where every side (length, width, and height) is exactly 2 units long, the total volume of that cube is calculated by multiplying those three dimensions together (2 × 2 × 2). The resulting volume is 8 cubic units.
Basic Rules Applied to 23
Multiplying with 23
Multiply 23 by another power of 2 by adding the exponents.
$$2^3 \times 2^4 = 2^{3+4} = 2^7 = 128$$Dividing with 23
Divide a larger power of 2 by 23 by subtracting the exponents.
$$\frac{2^6}{2^3} = 2^{6-3} = 2^3 = 8$$Negative Exponent (2-3)
A negative exponent turns the number into a fraction.
$$2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125$$
