Question

select the correct answer.

simplify the expression so there is only one positive power for the base, -5.

((-5)^7 \div (-5)^2)

• (\frac{1}{5^9})
• ((-5)^9)
• ((-5)^5)
• (\frac{1}{5^5})

Explanation:

Identify the given expression and rule

$$ (-5)^7 \div (-5)^2 $$

$$ \frac{a^m}{a^n} = a^{m-n} $$

Apply the quotient rule

$$ (-5)^{7-2} $$

Simplify the exponent

$$ (-5)^5 $$

Answer:

• (A) \(\frac{1}{5^9}\)
• (B) \((-5)^9\)
• (C) \((-5)^5\) (Correct answer)
• (D) \(\frac{1}{5^5}\)