Skill: Apply the quotient rule for powers

Explanation and Free Practice Resources

For powers with the same nonzero base, dividing means subtracting the exponents: $a^m \div a^n=a^{m-n}$ , because common factors in the numerator and denominator cancel; when exponents are equal, the quotient is $1$ . This applies to numerical and simple algebraic expressions with whole-number exponents and supports simplifying scientific notation; exponents are not divided. Cases resulting in negative exponents or requiring more advanced exponent laws are outside this level.

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Detailed Explanation: Apply the quotient rule for powers

When you divide powers with the same nonzero base, keep the base and subtract the exponents:

a^m \div a^n=a^{m-n}

This works because matching factors cancel.

Example:

\frac{5^6}{5^2}

Step 1: Subtract the exponents.

5^{6-2}

Step 2: Simplify the exponent.

5^4

Step 3: Evaluate if needed.

5^4=625

So,

\boxed{\frac{5^6}{5^2}=5^4=625}

Remember: subtract the exponents; do not divide them. If the exponents are equal, the quotient is $1$ , because all the matching factors cancel.

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Exponents - Division - Positive by Positive to Positive

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