From 599e5bb3b9cf774d4c3680644cf4bd0596fd34c0 Mon Sep 17 00:00:00 2001
From: altaf-creator <dev@altafcreator.com>
Date: Thu, 18 Jul 2024 10:39:11 +0700
Subject: Start migrating (and rewriting) lessons, NEW FEATURE: quizzes
 (unfinished)

---
 lessons/matematika/1-exponents/1.md | 41 +++++++++++++++++++++++++++++--------
 1 file changed, 33 insertions(+), 8 deletions(-)

(limited to 'lessons/matematika/1-exponents/1.md')

diff --git a/lessons/matematika/1-exponents/1.md b/lessons/matematika/1-exponents/1.md
index b8224b2..16bf26b 100644
--- a/lessons/matematika/1-exponents/1.md
+++ b/lessons/matematika/1-exponents/1.md
@@ -7,13 +7,15 @@
 
 # Exponent Operations
 ## Multiplication
-If an exponented number is multiplied by another exponented number, the exponents would be summed together (instead of being multiplied)  
+If an exponented number is multiplied by another exponented number, the
+exponents would be summed together (instead of being multiplied)  
 
 \\( a^x \times b^y = (a \times b)^{x + y} \\)
 * \\( 10^4 \times 2^2 = (10 \times 2)^{4 + 2} = 20^6 \\)
 
 ## Division
-If an exponented number is multiplied by another exponented number, the exponents would be subtracted together (instead of being divided)  
+If an exponented number is multiplied by another exponented number, the
+exponents would be subtracted together (instead of being divided)  
 
 \\( a^x \div b^y = (a \div b)^{x - y} \\)
 * \\( 10^3 \div 2^4 = (10 \div 2)^{(4 - 2)} = 5^2 = 25 \\)
@@ -35,13 +37,36 @@ If a number is raised to the power of **zero**, the result is **one**.
 * \\( 69.420^0 = 1 \\)
 
 ## Negative Exponent
-If a number is raised to a negative power, also called as an inverse, it would be equal to...
+If a number is raised to a negative power, also called as an inverse, it would
+be equal to...
 
 \\( a^{-b} = \dfrac{1}{a^b} \\)
 
-
 ## Fractional Exponent
-
-# Examples
-
-## Exponential Equation
+**Denominator (y)** root of the **number (a)** to the power of the **Numerator (x)**.
+
+\\( a^{\frac{x}{y}} = \sqrt[y]{a^x} \\)
+* \\( 5^{\frac{1}{2}} = \sqrt[2]{5} \\)
+* \\( 7^{\frac{2}{3}} = \sqrt[3]{7^2} \\)
+
+# Exponential Equation
+1. $$
+\begin{aligned}
+2^{x + 5} &= 64 \\\\
+2^{x + 5} &= 2^6 &\leftarrow\textnormal{ you can change 64 into an exponented two (}2^x\textnormal{)} \\\\
+x + 5 &= 6 &\textnormal{eliminate the 2s} \\\\
+x &= 6 - 5 \\\\
+&= 1
+\end{aligned}
+$$
+1. $$
+\begin{aligned}
+16^{x + 2} &= 2^5 \\\\
+(2^4)^{x + 2} &= 2^5 \\\\
+2^{4x + 8} &= 2^5 \\\\
+4x + 8 &= 5 \\\\
+4x &= 5 - 8 \\\\
+4x &= -3 \\\\
+x &= -\dfrac{3}{4}
+\end{aligned}
+$$
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