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HomeHomework HelpmathematicsLaws of Integral Indices

Laws of Integral Indices

The mathematical rules and principles governing the manipulation of algebraic expressions with integral indices, including simplification, distribution of powers, and separation of coefficients

beginner
2 hours
Mathematics
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Overview

The laws of integral indices are essential rules in mathematics that simplify the manipulation of powers. Understanding these laws allows students to perform calculations more efficiently and solve complex equations with ease. The key laws include the product of powers, quotient of powers, power of ...

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Key Terms

Exponent
A number that shows how many times to multiply the base by itself.

Example: In 2^3, 3 is the exponent.

Base
The number that is being multiplied in an exponent expression.

Example: In 2^3, 2 is the base.

Power
The result of raising a base to an exponent.

Example: 2^3 equals 8, so 8 is the power.

Product of Powers
When multiplying two powers with the same base, add the exponents.

Example: a^m * a^n = a^(m+n).

Quotient of Powers
When dividing two powers with the same base, subtract the exponents.

Example: a^m / a^n = a^(m-n).

Power of a Power
When raising a power to another power, multiply the exponents.

Example: (a^m)^n = a^(m*n).

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Key Concepts

Product of PowersQuotient of PowersPower of a PowerZero Exponent Rule