Simplify and write the following in the exponential form:
`3^(3)xx2^(2)+2^(2)xx5^(0)`

Answer

To simplify the expression \(3^{3} \times 2^{2} + 2^{2} \times 5^{0}\) and write it in exponential form, we can follow these steps:

### Step 1: Write down the expression
We start with the given expression:
\[ 3^{3} \times 2^{2} + 2^{2} \times 5^{0} \]

### Step 2: Simplify \(5^{0}\)
Recall that any number raised to the power of 0 is equal to 1. Therefore:
\[ 5^{0} = 1 \]
Now we can rewrite the expression:
\[ 3^{3} \times 2^{2} + 2^{2} \times 1 \]
This simplifies to:
\[ 3^{3} \times 2^{2} + 2^{2} \]

### Step 3: Factor out \(2^{2}\)
Next, we can factor \(2^{2}\) out of both terms:
\[ 2^{2} \times (3^{3} + 1) \]

### Step 4: Calculate \(3^{3} + 1\)
Now we need to calculate \(3^{3}\):
\[ 3^{3} = 27 \]
So, we have:
\[ 3^{3} + 1 = 27 + 1 = 28 \]
Now we can rewrite the expression:
\[ 2^{2} \times 28 \]

### Step 5: Write \(28\) in terms of its prime factors
Next, we can express \(28\) as a product of its prime factors:
\[ 28 = 4 \times 7 = 2^{2} \times 7 \]
Substituting this back into the expression gives us:
\[ 2^{2} \times (2^{2} \times 7) \]

### Step 6: Combine the powers of \(2\)
Now we can combine the powers of \(2\):
\[ 2^{2} \times 2^{2} \times 7 = 2^{4} \times 7 \]

### Final Answer
Thus, the simplified expression in exponential form is:
\[ 2^{4} \times 7 \]

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