Questions: Order the expressions by choosing >, <, or =. 2^3 × 2^2 □ 2^6

Transcript text: Order the expressions by choosing $>,<$, or $=$. $2^{3} \times 2^{2}$ $\square$ $2^{6}$

Solution

Step 1: Simplify the Expressions

First, simplify the expression $2^3 \times 2^2$.

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

Now, compare $2^5$ with $2^6$.

Step 2: Compare the Expressions

We have:

Since $32 < 64$, we have:

\[ 2^5 < 2^6 \]

The expression $2^3 \times 2^2$ is less than $2^6$. Therefore, the correct order is:

\[ 2^3 \times 2^2 \, \boxed{<} \, 2^6 \]

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