Question

Order the expressions by choosing <, >, =.

2² x 5² ____ 10²
5⁵ x 2² ____ 2¹⁰
2⁵ x 5² _____ 10¹⁰

Answer 1

The expressions compare as follows: 2² x 5² equals 10², 5⁵ x 2² is less than 2¹⁰, and 2⁵ x 5² equals 10¹⁰. The ordering uses the properties of exponents to evaluate and compare the expressions.

Step-by-step explanation:

The question involves comparing expressions with exponents by ordering them using the symbols <, >, or =. By performing the exponentiation, we can find which expressions are equivalent or which is greater or smaller. Here are the steps to compare the given expressions:

• 2² x 5² = (2 x 5)² = 10²
• 5⁵ x 2² = (5 x 2¹⁰)² = 2¹⁰
• 2⁵ x 5² = (2µ x 5)¹⁰ = 10¹⁰

Now, we can order the expressions:

• 2² x 5² = 10² because they are both the square of 10.
• 5⁵ x 2² < 2¹⁰ because 5⁵ (3125) is less than 2¹⁰ (1024).
• 2⁵ x 5² = 10¹⁰ because when you multiply exponents, you just multiply the two numbers being raised to a power which in this case are 2⁵ (32) x 5² (25) giving us 10¹⁰ (10000000000).