To find the missing exponent in the equation [tex]\( 5.6 \times 10^{\square} = 56,000 \)[/tex], follow these steps:
1. Write the equation given:
[tex]\[
5.6 \times 10^{\square} = 56,000
\][/tex]
2. Isolate the [tex]\( 10^{\square} \)[/tex] term:
Divide both sides of the equation by 5.6:
[tex]\[
10^{\square} = \frac{56,000}{5.6}
\][/tex]
3. Simplify the right-hand side:
Calculate [tex]\( \frac{56,000}{5.6} \)[/tex]:
[tex]\[
10^{\square} = 10,000
\][/tex]
4. Express 10,000 as a power of 10:
Recall that [tex]\( 10,000 = 10^4 \)[/tex]:
[tex]\[
10^{\square} = 10^4
\][/tex]
5. Equate the exponents:
Since the bases (10) are the same, the exponents must be equal:
[tex]\[
\square = 4
\][/tex]
Therefore, the missing exponent is [tex]\( 4 \)[/tex].
The correct option is:
4
