Sullivan Bowman
04/07/2023 · Senior High School
Simplify the following. Assume that variables in the exponents represent integers and that all other variables are not 0 \( \frac{\left(y^{2 a}\right)^{7}}{y^{a-6}} \)
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Step-by-step Solution
To simplify the expression \( \frac{\left(y^{2 a}\right)^{7}}{y^{a-6}} \), we can start by applying the power of a power property of exponents, which states that \((x^m)^n = x^{m \cdot n}\).
1. Simplify the numerator:
\[
\left(y^{2a}\right)^{7} = y^{2a \cdot 7} = y^{14a}
\]
2. Now, rewrite the expression:
\[
\frac{y^{14a}}{y^{a-6}}
\]
3. Next, we can use the quotient of powers property, which states that \(\frac{x^m}{x^n} = x^{m-n}\):
\[
y^{14a - (a - 6)} = y^{14a - a + 6} = y^{13a + 6}
\]
Thus, the simplified expression is:
\[
\boxed{y^{13a + 6}}
\]
Quick Answer
\( y^{13a + 6} \)
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