Simplifying expressions is a key principle in the realm of algebra. It entails breaking down an algebraic expression to its most basic form. This process might involve aggregating similar terms, adhering to the sequence of operations, and employing mathematical properties such as the distributive or commutative property. Mastering this concept is crucial for efficient equation solving.
| Topic | Problem | Solution |
|---|---|---|
| None | $\left(\frac{3^{6}}{3^{2}}\right)^{\frac{1}{2}}=$ | Simplify the division inside the parentheses. According to the rule of exponents, when you divide t… |
| None | Simplify the expression. \[ 2+3[10(7 \cdot 5-30)-… | Perform the operation inside the innermost parentheses, which is the multiplication and subtraction… |
| None | $(6 \times(-6)) \div((-8)+(-2)-4+2) \div(-3)$ | Given the mathematical expression $(6 \times(-6)) \div((-8)+(-2)-4+2) \div(-3)$, we need to solve i… |
| None | Simplify. \[ \frac{5^{2}+2^{2}-1^{2}}{8 \div 2 \c… | Simplify the numerator: \(5^{2}+2^{2}-1^{2} = 25+4-1 = 28\) |
| None | Express the geometric sum using summation notatio… | This is a geometric series where each term is 4 times the previous term. The first term is 1 and th… |
| None | Express the arithmetic sum using summation nota \… | We are given an arithmetic series where the first term (a) is 9, the last term (l) is 123, and the … |
| None | Use properties of logarithms to expand the logari… | Use properties of logarithms to expand the logarithmic expression as much as possible. Where possib… |
| None | Reduce the expression using scientific notation a… | The problem is asking to add two numbers that are in scientific notation. The first number is \(4 \… |
| None | e un seul logarithme, l'expression suivante: \[ 2… | Apply property 1: \( 10\log{x} - 12\log{2x^3} + 12\log{4x^4} \) |
| None | $\log _{7} 9+\log _{7} 4$ | Use the logarithm property: \(\log_{a} b + \log_{a} c = \log_{a} (b \cdot c)\) |