Question
Simplify the expression. Write the result using positive exponents only. Assume that all bases are not equal to 0 . \[ \frac{x^{7} x^{6}}{x^{2}} \]
Ask by Blake Wilson. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \( x^{11} \).
Solution
To simplify the expression \(\frac{x^{7} x^{6}}{x^{2}}\), follow these steps:
1. **Multiply the powers in the numerator:**
\[
x^{7} \times x^{6} = x^{7+6} = x^{13}
\]
2. **Divide by \(x^{2}\):**
\[
\frac{x^{13}}{x^{2}} = x^{13-2} = x^{11}
\]
The simplified expression with positive exponents is:
\[
x^{11}
\]
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Simplify this solution Bonus Knowledge
To simplify the expression \(\frac{x^{7} x^{6}}{x^{2}}\), we first apply the rule of exponents that states when multiplying like bases, we add the exponents. Thus, we can combine the \(x^7\) and \(x^6\): \[ x^{7} x^{6} = x^{7+6} = x^{13} \] Now the expression becomes: \[ \frac{x^{13}}{x^{2}} \] Next, again we use the rule of exponents for division, which states that when dividing like bases, we subtract the exponents: \[ \frac{x^{13}}{x^{2}} = x^{13-2} = x^{11} \] So, the simplified expression is: \[ x^{11} \]
