Questions: Write two equivalent expressions using exponent laws.

Transcript text: Write two equivalent expressions using exponent laws.

Solution

Solution Steps

Step 1: Define the Expressions

We start by defining the base \( a = 2 \) and the exponents \( m = 3 \) and \( n = 4 \).

Step 2: Apply the Product of Powers Property

Using the product of powers property, we can express the multiplication of the same base with different exponents as: \[ a^m \cdot a^n = 2^3 \cdot 2^4 \] Calculating this gives us: \[ 2^3 \cdot 2^4 = 128 \]

Step 3: Apply the Power of a Power Property

Using the power of a power property, we can combine the exponents: \[ (a^m)^n = a^{m+n} = 2^{3+4} = 2^7 \] Calculating this also results in: \[ 2^7 = 128 \]

Final Answer

Both expressions are equivalent and yield the same result: \[ \boxed{128} \]

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