Combine the following expressions.
`7^(5)xx49^(8)`

Answer

To combine the expressions \( 7^5 \times 49^8 \), we can follow these steps:

### Step 1: Rewrite 49 in terms of base 7
We know that \( 49 \) can be expressed as \( 7^2 \). Therefore, we can rewrite the expression as:
\[ 49^8 = (7^2)^8 \]

### Step 2: Apply the power of a power rule
Using the exponent rule \( (a^m)^n = a^{m \cdot n} \), we can simplify \( (7^2)^8 \):
\[ (7^2)^8 = 7^{2 \cdot 8} = 7^{16} \]

### Step 3: Substitute back into the expression
Now we can substitute \( 49^8 \) back into the original expression:
\[ 7^5 \times 49^8 = 7^5 \times 7^{16} \]

### Step 4: Apply the product of powers rule
Using the rule \( a^m \times a^n = a^{m+n} \), we can combine the powers:
\[ 7^5 \times 7^{16} = 7^{5 + 16} = 7^{21} \]

### Final Answer
Thus, the combined expression is:
\[ \boxed{7^{21}} \]

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