Question
Evaluate \( (5^{2})^{0} + (10^{3})^{0} \)
Ask by Wilson Ramirez. in South Africa
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The expression evaluates to 2.
Solution
To evaluate the expression \( (5^{2})^{0} + (10^{3})^{0} \), let's break it down step by step:
1. **Understanding Exponents:**
- Any non-zero number raised to the power of 0 is equal to 1. In mathematical terms, for any \( a \neq 0 \):
\[
a^0 = 1
\]
2. **Applying the Rule:**
- Calculate each part of the expression separately:
\[
(5^{2})^{0} = 5^{2 \times 0} = 5^0 = 1
\]
\[
(10^{3})^{0} = 10^{3 \times 0} = 10^0 = 1
\]
3. **Adding the Results:**
- Now, add the two results together:
\[
1 + 1 = 2
\]
**Final Answer:**
**2**
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Simplify this solution The Deep Dive
To evaluate the expression \( (5^{2})^{0} + (10^{3})^{0} \), we can use the property of exponents that states any non-zero number raised to the power of zero equals one. So we calculate each part: 1. \( (5^{2})^{0} = 1 \) (since \( 5^{2} \) is a non-zero number) 2. \( (10^{3})^{0} = 1 \) (since \( 10^{3} \) is also a non-zero number) Now, we can sum them up: \[ (5^{2})^{0} + (10^{3})^{0} = 1 + 1 = 2 \] Therefore, the final result is \( \boxed{2} \).
