Questions: Enter the value of the exponent n for the equation 2^8 * 2^n=2^11

Transcript text: Enter the value of the exponent $n$ for the equation $2^{8} \cdot 2^{n}=2^{11}$

Solution

Solution Steps

To solve the equation $2^{8} \cdot 2^{n} = 2^{11}$, we can use the property of exponents that states $a^m \cdot a^n = a^{m+n}$. This allows us to combine the exponents on the left side of the equation. Once combined, we can set the exponents equal to each other since the bases are the same, and solve for $n$.

Step 1: Combine Exponents

We start with the equation: \[ 2^{8} \cdot 2^{n} = 2^{11} \] Using the property of exponents $a^m \cdot a^n = a^{m+n}$, we can rewrite the left side: \[ 2^{8+n} = 2^{11} \]

Step 2: Set Exponents Equal

Since the bases are the same, we can set the exponents equal to each other: \[ 8 + n = 11 \]

Step 3: Solve for $n$

To find $n$, we subtract 8 from both sides: \[ n = 11 - 8 \] This simplifies to: \[ n = 3 \]