Question
Find the numerical equivalent of \( 8^{1} \cdot 8^{3} \cdot \) (1 point) 512 4,096 \( 8^{4} \) Check answer Remaining Attempts : 3
Ask by Gibbs Warren. in the United States
Feb 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The numerical equivalent is 4,096.
Solution
Recall the exponent rule: When you multiply numbers with the same base, you add the exponents. Here we have:
8¹ · 8³ = 8^(1+3) = 8⁴
Now, calculate 8⁴:
8 × 8 = 64
64 × 8 = 512
512 × 8 = 4096
Thus, the numerical equivalent is 4096.
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Simplify this solution The Deep Dive
To simplify \( 8^{1} \cdot 8^{3} \), you can use the property of exponents that states \( a^{m} \cdot a^{n} = a^{m+n} \). Here, \( 1 + 3 = 4 \). So, \( 8^{1} \cdot 8^{3} = 8^{4} \). Now, to find the numerical equivalent of \( 8^{4} \), you compute \( 8 \times 8 \times 8 \times 8 \), which is \( 4096 \). The correct answer is \( 4,096 \).
