Paul Parry
12/29/2023 · Senior High School
\begin{tabular}{l|l}\( \frac{7.6^{3}}{7.6^{8}} \) & Quotient of Powers Law \\ - Power of a Quotient Law \\ - Zero Exponent Law \end{tabular}
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Step-by-step Solution
To simplify the expression \( \frac{7.6^{3}}{7.6^{8}} \), we can use the Quotient of Powers Law, which states that when dividing two powers with the same base, we subtract the exponents:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, we have:
\[
\frac{7.6^{3}}{7.6^{8}} = 7.6^{3-8} = 7.6^{-5}
\]
Thus, the correct law to apply here is the **Quotient of Powers Law**.
The other laws mentioned, the Power of a Quotient Law and the Zero Exponent Law, do not apply directly to this expression.
So, the final answer is:
\[
\frac{7.6^{3}}{7.6^{8}} = 7.6^{-5}
\]
And the relevant law used is the **Quotient of Powers Law**.
Quick Answer
The expression simplifies to \( 7.6^{-5} \) using the Quotient of Powers Law.
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