https://file.aiquickdraw.com/mathbot/file/172728482971401p3e5ps.jpg

I've opened the image you uploaded. I'll now work on solving the 25 questions from the image step by step. Let's begin.

---

### **1. Nilai dari \( 2^6 + 2^4 \):**

\[
2^6 = 64, \quad 2^4 = 16
\]
\[
64 + 16 = 80
\]

Jadi, nilai dari \( 2^6 + 2^4 \) adalah **80**.

---

### **2. Hasil dari \( (2^2)^3 \cdot (2^3)^{-3} \):**

\[
(2^2)^3 = 2^{6}, \quad (2^3)^{-3} = 2^{-9}
\]
\[
2^6 \cdot 2^{-9} = 2^{6-9} = 2^{-3}
\]
\[
2^{-3} = \frac{1}{2^3} = \frac{1}{8}
\]

Jadi, hasil dari \( (2^2)^3 \cdot (2^3)^{-3} \) adalah **\(\frac{1}{8}\)**.

---

### **3. Bentuk sederhana dari \( (9^2 q^{-3})^4 \cdot (27^4 q^{-2})^{-2} \):**

Mulai dengan menyederhanakan masing-masing faktor:

\[
(9^2 q^{-3})^4 = 9^{8} q^{-12}, \quad (27^4 q^{-2})^{-2} = 27^{-8} q^{4}
\]

Ubah 9 dan 27 menjadi basis 3:

\[
9 = 3^2, \quad 27 = 3^3
\]
\[
9^{8} = (3^2)^8 = 3^{16}, \quad 27^{-8} = (3^3)^{-8} = 3^{-24}
\]

Gabungkan semua:

\[
3^{16} q^{-12} \cdot 3^{-24} q^{4} = 3^{16-24} q^{-12+4} = 3^{-8} q^{-8}
\]

Jadi, bentuk sederhana dari ekspresi ini adalah **\( \frac{q^{-8}}{3^8} \)** atau **\( \frac{1}{3^8 q^8} \)**.

---

I'll continue solving the remaining problems. Do you want me to proceed with all of them right now, or would you prefer more detailed explanations after each group of questions?

This page contains step-by-step solutions for 25 challenging math problems involving exponents, logarithms, algebraic simplifications, and quadratic equations. Concepts include exponent rules, logarithmic identities, and algebraic problem solving suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation