Problem Analysis:
The task involves working with exponents (powers) and ordering the results from smallest to largest. The specific part of the problem we need to focus on is:
Work out these exponents, then put them in order, from smallest to largest:
- \( 5^6 \)
- \( 2^9 \)
- \( 6^4 \)
- \( 9^3 \)
- \( 10^4 \)
- \( 7^5 \)
Step-by-Step Solution:
#### 1. Calculate Each Exponent:
We will calculate each exponent individually.
-
\( 5^6 \):
\[
5^6 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 15625
\]
-
\( 2^9 \):
\[
2^9 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 512
\]
-
\( 6^4 \):
\[
6^4 = 6 \times 6 \times 6 \times 6 = 1296
\]
-
\( 9^3 \):
\[
9^3 = 9 \times 9 \times 9 = 729
\]
-
\( 10^4 \):
\[
10^4 = 10 \times 10 \times 10 \times 10 = 10000
\]
-
\( 7^5 \):
\[
7^5 = 7 \times 7 \times 7 \times 7 \times 7 = 16807
\]
#### 2. List the Results:
Now, we have the values for each exponent:
- \( 5^6 = 15625 \)
- \( 2^9 = 512 \)
- \( 6^4 = 1296 \)
- \( 9^3 = 729 \)
- \( 10^4 = 10000 \)
- \( 7^5 = 16807 \)
#### 3. Order the Results from Smallest to Largest:
We compare the values and arrange them in ascending order:
- \( 2^9 = 512 \) (smallest)
- \( 9^3 = 729 \)
- \( 6^4 = 1296 \)
- \( 10^4 = 10000 \)
- \( 5^6 = 15625 \)
- \( 7^5 = 16807 \) (largest)
Final Answer:
\[
\boxed{2^9, 9^3, 6^4, 10^4, 5^6, 7^5}
\]
Parent Tip: Review the logic above to help your child master the concept of 9th grade math worksheet with answers.
