Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 3^{3} \times 3^{7} = 59049 \)
Solution
Calculate the value by following steps:
- step0: Calculate:
\(3^{3}\times 3^{7}\)
- step1: Multiply:
\(3^{3+7}\)
- step2: Add the numbers:
\(3^{10}\)
- step3: Evaluate the power:
\(59049\)
To solve the expression \( 3^{3} \times 3^{7} \), we can use the property of exponents that states \( a^{m} \times a^{n} = a^{m+n} \).
1. Here, we have:
\[
3^{3} \times 3^{7} = 3^{3+7}
\]
2. Now, we add the exponents:
\[
3 + 7 = 10
\]
3. Therefore, we can rewrite the expression as:
\[
3^{10}
\]
4. Now, we calculate \( 3^{10} \):
\[
3^{10} = 59049
\]
Thus, the final answer is \( 59049 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
When you multiply numbers with the same base, you add their exponents. So, \( 3^3 \times 3^7 = 3^{3+7} = 3^{10} \). To make it even sweeter, if you compute \( 3^{10} \), you'll get 59,049! Isn't math marvelous? Not only does this property of exponents simplify calculations, but it also shows up in various fields like computer science, where efficiency in algorithms often relies on understanding how to manipulate these fundamental rules. So, the next time you're building an app or crunching numbers, remember how useful these exponent rules can be!
