5 to the power of X= 25 to the power of -8

We start with the equation:

\[
5^x = 25^{-8}
\]

### Step 1: Express 25 as a power of 5
We know that \(25 = 5^2\), so we can rewrite the equation as:

\[
5^x = (5^2)^{-8}
\]

### Step 2: Simplify the right-hand side
Using the property \((a^m)^n = a^{m \cdot n}\), we can simplify the right-hand side:

\[
5^x = 5^{2 \cdot (-8)} = 5^{-16}
\]

### Step 3: Set the exponents equal
Since the bases are the same (both are powers of 5), we can equate the exponents:

\[
x = -16
\]

Thus, the solution is:

\[
x = -16
\]

Would you like more details or have any questions?

Here are five related questions to explore:
1. What is \( 5^x = 25^x \) and how does it compare?
2. How do you solve \( 5^x = 125^y \)?
3. How do the properties of exponents apply to negative exponents?
4. How can we solve equations with fractional exponents?
5. How do we approach exponential equations with different bases?

**Tip**: When solving exponential equations, always check if the terms can be rewritten with the same base—it simplifies the process significantly!

5 to the power of X = 25 to the power of -8

Learn how to solve the exponential equation 5^x = 25^(-8) by expressing 25 as a power of 5. This step-by-step solution simplifies the equation and applies the properties of exponents, making it suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation