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Which exponent is missing from this equation?

[tex]\[ 5.6 \times 10^{\square} = 56,000 \][/tex]

A. 5

B. 2

C. 4

D. 3


Sagot :

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