Power before sum and product
- Input
- 2 + 3 × 4²
- Expected output
- 50
4² = 16; 3 × 16 = 48; 2 + 48.
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numeric expressions with powers and square roots
Type powers with ^ or with the superscripts ² and ³, and roots with √, ∛ or sqrt. Powers and roots are solved before any multiplication, division, addition or subtraction in the same group, and the tool shows each one as its own step.
4² = 16; 3 × 16 = 48; 2 + 48.
8 + 9 − 4 = 13.
√25 = 5 and ∛27 = 3.
−(3²).
(−3) × (−3).
1 divided by 2³.
√1 = 1 and √4 = 2.
Groups first (parentheses, then brackets, then braces, always innermost outward). Inside each group: powers and roots; multiplications and divisions, left to right; additions and subtractions, left to right. Example: 2 + 3 × 4² = 2 + 3 × 16 = 2 + 48 = 50.
Before. Roots and powers share the highest level. In 3 × √16, the tool computes √16 = 4 and then 3 × 4 = 12.
Use ∛ or cbrt(27) for the cube root, ∜ for the fourth, and a superscript index before the radical, as in ⁵√32, for the rest. Raising to a fraction also works: 32^(1/5) = 2.
From 1 to 15 the squares are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196 and 225. The exact root of any of them appears as a whole number; the roots of 2, 3, 5, 6, 7, 8 and 10 are not exact.
The math uses exact integers and accepts exponents up to 10000, as long as the result stays under roughly 200 thousand bits. 99999999999³ comes out complete, with all 33 digits. Over the limit, the tool says the number would be too large.
Accepts parentheses, brackets and braces, × ÷ + −, powers (2^3 or 2³), roots (√9, ∛27, sqrt(16)), percent, absolute value |x|, decimals and fractions. 1/2 without spaces is the fraction; 1 / 2 with spaces is a division.
The exercise appears in the field with the solution hidden. Results for levels 1 to 3 are always whole numbers.
All the math happens in your browser. No expression is sent to any server.