Preparing your Lab
AllScienceTools
AllScienceTools
Exponents, Logs, Quadratics.
Mastering Algebra Rules is a key step in your Reference Materials journey. We built this Algebra Rules to be your personal study assistant—helping you solve problems step-by-step, verify your homework answers, and build confidence before exams.
This tool handles the computation, allowing you to focus on the underlying logic and problem-solving strategies. It is particularly useful for verifying hand-written work and exploring different problem scenarios instantly.
Instant, high-precision results
Mobile-friendly interface
Ad-free study environment
Step-by-step logical verification
Understanding Algebra Rules is fundamental. Our calculator uses standard algorithms aligned with academic curriculums to ensure the results match what you need for your classes.
| x^a · x^b = x^(a+b) |
| (x^a)^b = x^(ab) |
| x^a / x^b = x^(a-b) |
| x^(-a) = 1/x^a |
| (xy)^a = x^a y^a |
| √(xy) = √x · √y |
| x^(1/n) = ⁿ√x |
| y = log_b(x) ⇔ b^y = x | |
| log(xy) = log(x) + log(y) | |
| log(x/y) = log(x) - log(y) | |
| log(x^k) = k log(x) | |
| log_b(a) = ln(a) / ln(b) | Change of Base |
| a² - b² = (a - b)(a + b) | Diff of Squares |
| a³ - b³ = (a - b)(a² + ab + b²) | Diff of Cubes |
| a³ + b³ = (a + b)(a² - ab + b²) | Sum of Cubes |
| (a + b)² = a² + 2ab + b² | Perfect Sq |
| (a - b)² = a² - 2ab + b² | Perfect Sq |
For ax² + bx + c = 0
i = √(-1), i² = -1
Form: z = a + bi
Modulus: |z| = √(a² + b²)
Conjugate: z̅ = a - bi
Euler's Form: z = re^(iθ) = r(cosθ + isinθ)
| Circle | (x-h)² + (y-k)² = r² |
| Ellipse | (x-h)²/a² + (y-k)²/b² = 1 |
| Hyperbola | (x-h)²/a² - (y-k)²/b² = 1 |
| Parabola | y = a(x-h)² + k |