Express in exponent form with a prime number base: ((5^(a+1))(125))/(25^(2a))

To express the given expression in exponent form with a prime number base, we first rewrite each term in the expression using prime number bases.

The given expression is:

\[
\frac{(5^{a+1}) \cdot 125}{25^{2a}}
\]

Let's rewrite 125 and 25 using the prime number base \(5\):

- \(125 = 5^3\) because \(125 = 5 \times 5 \times 5 = 5^3\).
- \(25 = 5^2\) because \(25 = 5 \times 5 = 5^2\).

Now substitute these into the expression:

\[
\frac{(5^{a+1}) \cdot (5^3)}{(5^2)^{2a}}
\]

Simplify the exponents:

\[
\frac{5^{a+1 + 3}}{5^{4a}}
\]

Combine the exponents in the numerator:

\[
\frac{5^{a+4}}{5^{4a}}
\]

Now, use the property of exponents \(\frac{5^m}{5^n} = 5^{m-n}\) to simplify:

\[
5^{(a+4) - 4a}
\]

Simplify the exponent:

\[
5^{a + 4 - 4a} = 5^{4 - 3a}
\]

So, the expression in exponent form with a prime number base is:

\[
5^{4 - 3a}
\]

Would you like further details or have any questions? 

Here are 5 related questions to further expand on this concept:

1. How do you simplify an expression with multiple exponents of the same base?
2. What are the rules for multiplying and dividing exponents?
3. How do you convert a radical expression to exponent form?
4. What is the importance of expressing numbers with prime bases in mathematics?
5. How would you approach simplifying an expression with multiple variables in the exponents?

**Tip:** Remember that when dividing exponents with the same base, you subtract the exponents.

Learn how to express ((5^(a+1))(125))/(25^(2a)) in exponent form with a prime number base. This problem involves simplifying exponents and utilizing prime bases in mathematics. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation