Answer :
To simplify the expression \((x^5)(x^2)\), we use the properties of exponents. Specifically, when multiplying two exponential expressions with the same base, we add the exponents.
Here's the step-by-step solution:
1. Identify the base: In both \(x^5\) and \(x^2\), the base is \(x\).
2. Identify the exponents: The exponents are 5 and 2.
3. Add the exponents together: \(5 + 2\).
Therefore, \( (x^5)(x^2) = x^{5 + 2} = x^7 \).
So, the simplified expression is:
[tex]\[ x^7 \][/tex]
The correct answer is [tex]\( \boxed{x^7} \)[/tex] (Option C).
Here's the step-by-step solution:
1. Identify the base: In both \(x^5\) and \(x^2\), the base is \(x\).
2. Identify the exponents: The exponents are 5 and 2.
3. Add the exponents together: \(5 + 2\).
Therefore, \( (x^5)(x^2) = x^{5 + 2} = x^7 \).
So, the simplified expression is:
[tex]\[ x^7 \][/tex]
The correct answer is [tex]\( \boxed{x^7} \)[/tex] (Option C).
