https://file.aiquickdraw.com/mathbot/file/17268468491954tb3hocy.jpg

The problem asks to simplify the exponents in two expressions:

### a. \( 5^2 \times 5^3 \)

Since the base is the same (5), you can apply the rule of exponents for multiplication: 

\[
a^m \times a^n = a^{m+n}
\]

Thus,

\[
5^2 \times 5^3 = 5^{2+3} = 5^5
\]

### b. \( \left(\frac{1}{3}\right)^5 \times \left(\frac{1}{3}\right)^2 \)

Similarly, because the base is the same \( \frac{1}{3} \), apply the same rule of exponents:

\[
\left(\frac{1}{3}\right)^5 \times \left(\frac{1}{3}\right)^2 = \left(\frac{1}{3}\right)^{5+2} = \left(\frac{1}{3}\right)^7
\]

So the simplified expressions are:
- a. \( 5^5 \)
- b. \( \left(\frac{1}{3}\right)^7 \)

Would you like further explanation or details on exponent rules?

Here are 5 related questions you could explore:
1. What are the properties of exponents for division?
2. How do negative exponents affect the value of an expression?
3. What is the rule for raising a power to another power?
4. How do fractional exponents relate to radicals (square roots, cube roots, etc.)?
5. What happens if the base of the exponents is negative?

**Tip**: When multiplying or dividing exponents with the same base, you can simplify by adding or subtracting the exponents, respectively.

Sederhanakan bentuk pangkat di bawah ini! a. 5^2 × 5^3 b. (1/3)^5 × (1/3)^2

Learn how to simplify exponent expressions like 5^2 × 5^3 and (1/3)^5 × (1/3)^2 by applying the exponent multiplication rule. This problem focuses on key algebraic concepts and is suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation