Powers and exponent laws

Japanese school year: Junior high 1

What you learn

Learn the concept of powers representing repeated multiplication of the same number, their notation using exponents, and basic calculations. These skills form the foundation for working with algebraic expressions and equations. Confidence in performing multiplication with positive and negative numbers is helpful before beginning.

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Key points

This exponent rule states that when multiplying powers with the same base $a$ , add their exponents $m$ and $n$ . For example, $a^2 \times a^3 = a^{2+3} = a^5$ .

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

This rule states that when raising a power to another power, multiply the inside exponent $m$ by the outside exponent $n$ . For instance, $(a^2)^3 = a^{2 \times 3} = a^6$ .

(a^m)^n = a^{mn}

This rule states that raising a product $(ab)$ to the power of $n$ means raising each factor, $a$ and $b$ , to $n$ . For example, $(2x)^3 = 2^3 x^3 = 8x^3$ .

(ab)^n = a^n b^n

This rule states that when dividing powers with the same base $a$ , subtract the divisor's exponent $n$ from $m$ . For example, $a^5 \div a^2 = a^{5-2} = a^3$ .

a^m \div a^n = a^{m-n} \quad (a \neq 0)

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Practice 1Coming soon