$$ \frac{1 imes 10^{32} imes 1 imes 10^{20} imes 1 imes 10^{22}}{1 imes 10^{11} imes 1 imes 10^{12}}=1 imes 10^{?} $$ $$ \square=?= $$ product's exponent

Question

$$ \frac{1 	imes 10^{32} 	imes 1 	imes 10^{20} 	imes 1 	imes 10^{22}}{1 	imes 10^{11} 	imes 1 	imes 10^{12}}=1 	imes 10^{?} $$ $$ \square=?= $$ product's exponent

UpStudy AI · Accepted Answer

To find the exponent in the expression:

$$
\frac{1 \times 10^{32} \times 1 \times 10^{20} \times 1 \times 10^{22}}{1 \times 10^{11} \times 1 \times 10^{12}} = 1 \times 10^{\square}
$$

**Step 1: Simplify the Numerator**

Multiply the powers of 10 in the numerator by adding their exponents:

$$
10^{32} \times 10^{20} \times 10^{22} = 10^{32 + 20 + 22} = 10^{74}
$$

**Step 2: Simplify the Denominator**

Multiply the powers of 10 in the denominator by adding their exponents:

$$
10^{11} \times 10^{12} = 10^{11 + 12} = 10^{23}
$$

**Step 3: Divide the Numerator by the Denominator**

Subtract the exponent in the denominator from the exponent in the numerator:

$$
\frac{10^{74}}{10^{23}} = 10^{74 - 23} = 10^{51}
$$

**Final Result**

$$
\frac{1 \times 10^{32} \times 1 \times 10^{20} \times 1 \times 10^{22}}{1 \times 10^{11} \times 1 \times 10^{12}} = 1 \times 10^{51}
$$

Therefore, the value of $$ \square $$ is **51**.
$$ \square = 51 $$

\( \frac{1 \times 10^{32} \times 1 \times 10^{20} \times 1 \times 10^{22}}{1 \times 10^{11} \times 1 \times 10^{12}}=1 \times 10^{?} \) \( \square=?= \) product's exponent

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