How to apply subtraction index law when dividing powers with identical bases (with examples)
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The quotient law of exponentiation, also known as the division law of exponents, is one of the fundamental rules governing the manipulation of expressions with exponents. This law is used when you are dividing two expressions with the same base. The quotient law is stated as follows:
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
Here's an explanation of the quotient law:
When you have the same base (denoted by "a") raised to different exponents/indices (m and n), and you divide the two expressions, you can simplify the expression by subtracting the exponent in the denominator/divisor from the exponent in the numerator/divident.
For example:
a⁵ ÷ a² = a⁵⁻² = a³
This simplification follows the quotient law of exponentiation. It shows that when you divide a⁵ by a² (both with the same base a), you subtract the exponent in the denominator from the exponent in the numerator to get a³.
This law is a part of the broader set of exponent laws, which also include the product law, power law, zero exponent law, and negative exponent law. These laws are fundamental in algebra and provide rules for simplifying and manipulating expressions involving exponents.
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