Find the numerical equivalent of 8^1 ⋅8^3

Question

.(1 point)
Responses

84
8 to the 4th power

512
512

4096
4096

520

Answer 1

To solve \( 8^1 \cdot 8^3 \), we can apply the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

Here, \( m = 1 \) and \( n = 3 \):

\[ 8^1 \cdot 8^3 = 8^{1+3} = 8^4 \]

Now, we need to find \( 8^4 \):

\[ 8^4 = 8 \cdot 8 \cdot 8 \cdot 8 \]

Calculating step-by-step:

1. \( 8 \cdot 8 = 64 \)
2. \( 64 \cdot 8 = 512 \)
3. \( 512 \cdot 8 = 4096 \)

Thus, \( 8^4 = 4096 \).

So, the numerical equivalent of \( 8^1 \cdot 8^3 \) is:

4096