MathematicsClass 8Exponents and Powers

Laws of Exponents

Applying algebraic rules for multiplying and dividing terms with the same or different bases and exponents.

Class 8 · MathematicsCBSE & ICSE SOF IMO IOQM

Definition

The laws of exponents are fundamental rules that simplify algebraic expressions involving powers with the same base or exponent. These laws streamline multiplication, division, and the power of a power operations. They apply universally to all non-zero bases and integer exponents.

Key formula

a^m \times a^n = a^{m+n}

Worked examples

Multiply 2^3 \times 2^4 by adding the exponents to get 2^{3+4} = 2^7.

Simplify (3^2)^3 by multiplying the exponents to get 3^{2 \times 3} = 3^6.

Evaluate \frac{5^5}{5^2} by subtracting the exponents to get 5^{5-2} = 5^3 = 125.

Common mistakes

• Multiplying the exponents instead of adding them when multiplying two powers with the same base, such as writing 2^3 \times 2^4 as 2^{12}.
• Adding bases together when multiplying or dividing instead of keeping the base common and operating only on the exponents.

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