Use the Product Rule of Exponents to simplify the expression 24⋅22

.(1 point)

1 answer

To simplify the expression \( 24 \cdot 22 \) using the Product Rule of Exponents, we first rewrite each term with a base of 2:

\[ 24 = 2^3 \quad \text{(since } 2^3 = 8 \text{ and } 8 + 16 = 24\text{)} \] \[ 22 = 2^{2} \quad \text{(since } 2^{2} = 4\text{)} \]

Now, substituting these values into the original expression gives:

\[ 24 \cdot 22 = 2^3 \cdot 2^2 \]

According to the Product Rule of Exponents, when multiplying like bases, you add the exponents:

\[ 2^3 \cdot 2^2 = 2^{3 + 2} = 2^5 \]

Now, let's express \( 2^5 \):

\[ 2^5 = 32 \]

Thus, the simplified expression for \( 24 \cdot 22 \) is \( 32 \).