Simplify. Express your answer using positive exponents.

Question

(7t)(7t^7)

Answer 1

To simplify the expression \((7t)(7t^7)\), we can first multiply the coefficients (the numerical parts) and then the variables.

1. Multiply the coefficients: \[ 7 \times 7 = 49 \]

2. For the variable \(t\), use the property of exponents that states \(t^a \cdot t^b = t^{a+b}\): \[ t \cdot t^7 = t^{1+7} = t^8 \]

Now, combine both parts: \[ (7t)(7t^7) = 49t^8 \]

Thus, the simplified expression is: \[ \boxed{49t^8} \]