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Rewrite the expression as a fraction.

April 14, 2026Mathematics

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Answer

6 steps

Rewrite the expression as a fraction.
$\frac{56a^{-6}}{7a^{-4}}$
Separate the numerical coefficients and the variable terms.
$\left(\frac{56}{7}\right) \times \left(\frac{a^{-6}}{a^{-4}}\right)$
Simplify the numerical part.
$\frac{56}{7} = 8$
Apply the exponent rule for division, which states that $\frac{x^m}{x^n} = x^{m-n}$ .
$a^{-6 - (-4)}$
Simplify the exponent.
$a^{-6 + 4} = a^{-2}$
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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