Certainly! Let's simplify the given expression step by step.
The expression given is:
[tex]\[ 12^{-3} \cdot 12^{10} \cdot 12^0 \][/tex]
### Step 1: Simplify Each Term
1. Simplifying [tex]\( 12^{-3} \)[/tex]:
- The exponent [tex]\(-3\)[/tex] indicates that the term is a reciprocal raised to the power of 3.
- Therefore, [tex]\( 12^{-3} = \frac{1}{12^3} \)[/tex].
2. Simplifying [tex]\( 12^{10} \)[/tex]:
- This term remains as it is since the exponent is positive.
- So, [tex]\( 12^{10} \)[/tex] remains [tex]\( 12^{10} \)[/tex].
3. Simplifying [tex]\( 12^0 \)[/tex]:
- Any number raised to the power of 0 is 1.
- Therefore, [tex]\( 12^0 = 1 \)[/tex].
### Step 2: Combine Exponents
Since the base in each term is the same (12), we can combine the exponents by adding them:
[tex]\[ 12^{-3} \cdot 12^{10} \cdot 12^0 = 12^{-3 + 10 + 0} \][/tex]
### Step 3: Sum of the Exponents
Calculate the sum of the exponents:
[tex]\[ -3 + 10 + 0 = 7 \][/tex]
### Step 4: Simplify the Expression
Thus, we have:
[tex]\[ 12^{-3 + 10 + 0} = 12^7 \][/tex]
The simplified expression is:
[tex]\[ 12^7 \][/tex]
### Step 5: Evaluate [tex]\( 12^7 \)[/tex]
The value of [tex]\( 12^7 \)[/tex]:
[tex]\[ 12^7 = 35831808 \][/tex]
Therefore, the simplified form of the given expression is [tex]\(\boxed{12^7}\)[/tex].
Among the given options, the correct one is:
[tex]\[ 12^7 \][/tex]
