October 28, 2024

Multiplying Exponents Made Easy

Multiplying exponents is simple with the \textbf{product of powers rule}: if two terms have the same base, add their exponents. Product of Powers Rule If two expressions share the same base, we add the exponents: \[\begin{align*} a^m \cdot a^n = a^{m+n} \end{align*}\] Example: \[\begin{align*} x^2 \cdot x^5 = x^{2+5} = x^7 \end{align*}\] Why It Works…

Read article
Exponent Rules Explained

Madhavendra Thakur October 28, 2024 Introduction Exponents allow us to represent repeated multiplication in a concise way. Mastering the basic exponent rules helps simplify complex algebraic expressions, and is a key stepping stone to more complex areas of math. This guide presents the rules with step-by-step examples for clarity. 1. Exponent Rules 1.1 Product of…

Read article
Evaluating 2^5 in Simple Steps

In this blog, we’ll walk through how to evaluate the expression \( 2^5 \). Exponents are a fundamental concept in mathematics, and understanding them starts with examples like this. What Does $2^5$ Mean? The expression \( 2^5 \) means that we multiply the number 2 by itself a total of 5 times. More generally, an…

Read article
What is an integral?

Introduction Before diving into calculus and memorizing formulas, it is important to take a step back and understand what an integral actually means. What is an Integral? An integral, graphically, represents the area under a curve. You might be wondering why it’s useful to know the area under the curve. The reason is that the…

Read article
Understanding the Logarithm: $\log_a b$

\[\begin{align*} \displaystyle\boxed{\log_a b = x \text{ is equivalent to } a^x = b} \end{align*}\] What is $\log_a b$? This expression reads “log base a of b”. In mathematics, $\log_a b$ is called the logarithm of $b$ with base $a$. The logarithm $\log_a b$ answers the question: “What power do we need to raise $a$ to, in…

Read article
Log change of base

$$\boxed{\log_b a = \dfrac{\log_k a}{\log_k b}}$$ The change of base formula for logarithms states that any $\log_b a$ can be expressed as $\dfrac{\log_k a}{\log_k b}$ where $k$ is any positive number. This formula is often used when calculating logarithms with the base that is inconvenient. What is a logarithm? A logarithm $\log_b a$ asks the…

Read article