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Simplify the expression: [tex]\[ 7^x \times 7^3 \][/tex]
1. Expression: We start with the given expression [tex]\( 7^x \times 7^3 \)[/tex].
2. Properties of Exponents: We can simplify the expression using the rule of exponents which states that [tex]\( a^m \times a^n = a^{m+n} \)[/tex]. Here, the base [tex]\( a \)[/tex] is the same (7), so we can add the exponents. [tex]\[
7^x \times 7^3 = 7^{x+3}
\][/tex]
3. Simplified Expression: Therefore, the simplified form of [tex]\( 7^x \times 7^3 \)[/tex] is [tex]\( 7^{x+3} \)[/tex].
4. Alternative Representation: For better understanding, we can break it down with some specific values. For example, we know: [tex]\[
7^3 = 343
\][/tex]
5. Rewriting the Expression: Using the value [tex]\( 7^3 \)[/tex], we can rewrite the original expression as: [tex]\[
7^x \times 343
\][/tex]
6. Final Result: So we have two ways to represent the result: [tex]\[
7^x \times 7^3 = 343 \times 7^x \quad \text{or} \quad 7^x \times 7^3 = 7^{x+3}
\][/tex]
Putting it all together, the original expression [tex]\( 7^x \times 7^3 \)[/tex] can be represented as: [tex]\[
343 \times 7^x \quad \text{or simply} \quad 7^{x+3}
\][/tex]
These are two equivalent representations of the given expression.
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