Question

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

Answer 1

To simplify the expression \( 24 \cdot 22 \) using the Product Rule of Exponents, we first need to recognize that we can express the numbers in terms of exponents.

Recall that:
\[
a^m \cdot a^n = a^{m+n}
\]

We can rewrite \( 24 \) as \( 2^4 \) and \( 22 \) as \( 2^2 \):
\[
24 = 2^4 \quad \text{and} \quad 22 = 2^2
\]

Now we substitute these values into the original expression:
\[
24 \cdot 22 = 2^4 \cdot 2^2
\]

Using the Product Rule of Exponents:
\[
2^4 \cdot 2^2 = 2^{4+2} = 2^6
\]

So, the simplified form of the expression \( 24 \cdot 22 \) is:
\[
2^6
\]

To express this in numerical form, we calculate \( 2^6 \):
\[
2^6 = 64
\]

Thus, the final answer is:
\[
24 \cdot 22 = 64
\]