Rewrite the expression as a fraction.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Rewrite the expression as a fraction.
$$ \frac{56a^{-6}}{7a^{-4}} $$
Step 2: Separate the numerical coefficients and the variable terms.
$$ \left(\frac{56}{7}\right) \times \left(\frac{a^{-6}}{a^{-4}}\right) $$
Step 3: Simplify the numerical part.
$$ \frac{56}{7} = 8 $$
Step 4: Apply the exponent rule for division, which states that $\frac{x^m}{x^n} = x^{m-n}$.
$$ a^{-6 - (-4)} $$
Step 5: Simplify the exponent.
$$ a^{-6 + 4} = a^{-2} $$
Step 6: Combine the simplified numerical and variable parts.
$$ 8a^{-2} $$
Comparing this result with the given options:
A $8a^{-10}$
B $8a^{-8}$
C $8a^{-2}$
D $8a^{2}$
E $8a^{10}$
The correct option is C.
The final answer is $\boxed{\text{C } 8a^{-2}}$.
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