To determine the value of \( a \) for which \( 8 \times 10^3 \) is 10 times larger than \( 8 \times 10^a \), we can set up the equation:
\[ 8 \times 10^3 = 10 \times (8 \times 10^a) \]
First, we simplify the right-hand side:
\[ 8 \times 10^3 = 80 \times 10^a \]
Next, we divide both sides by 8:
\[ 10^3 = 10 \times 10^a \]
This simplifies to:
\[ 10^3 = 10^{a+1} \]
Now, we can equate the exponents (since the bases are the same):
\[ 3 = a + 1 \]
Solving for \( a \):
\[ a = 3 - 1 = 2 \]
Thus, the value of \( a \) is
\[ \boxed{2} \]
4 answers