Question
Question 30 Simplify the expression. \( \left.\frac{x^{26} y^{78}}{x^{16} y^{15}}=\square\right\rangle \)
Ask by Ingram Brooks. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x^{10} y^{63} \)
Solution
To simplify the expression \( \frac{x^{26} y^{78}}{x^{16} y^{15}} \), you can use the properties of exponents which state that when you divide like bases, you subtract the exponents:
\[
\frac{x^{a}}{x^{b}} = x^{a-b} \quad \text{and} \quad \frac{y^{c}}{y^{d}} = y^{c-d}
\]
Applying these rules:
1. **Simplify the \(x\) terms:**
\[
\frac{x^{26}}{x^{16}} = x^{26-16} = x^{10}
\]
2. **Simplify the \(y\) terms:**
\[
\frac{y^{78}}{y^{15}} = y^{78-15} = y^{63}
\]
Putting it all together:
\[
\frac{x^{26} y^{78}}{x^{16} y^{15}} = x^{10} y^{63}
\]
**Answer:** \(x^{10}\, y^{63}\)
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Simplify this solution Mind Expander
To simplify the expression \( \frac{x^{26} y^{78}}{x^{16} y^{15}} \), we can start by applying the quotient rule of exponents, which states that \( \frac{a^m}{a^n} = a^{m-n} \). For \( x \): \[ \frac{x^{26}}{x^{16}} = x^{26-16} = x^{10} \] For \( y \): \[ \frac{y^{78}}{y^{15}} = y^{78-15} = y^{63} \] Putting it all together, the simplified expression is \( x^{10} y^{63} \).
