Algebra 1

Dec 13, 2025

418

1 page

Laws of Exponents: Summary and Review of Key Rules

mia! @mdotti.ny

Exponent rules make working with powers much simpler! Instead of doing lengthy calculations, these rules give us shortcuts... Show more

Laws of Exponents

When you see expressions with the same base, you can use exponent rules to simplify them quickly. For the product of powers, simply add the exponents when multiplying terms with the same base $a^m \cdot a^n = a^{m+n}$ . For example, $2^4 \cdot 2^3 = 2^{4+3} = 2^7$ or $(2y)(4y^3) = 8y^4$ .

The quotient of powers rule works by subtracting exponents when dividing terms with the same base $\frac{a^m}{a^n} = a^{m-n}$ . For instance, $\frac{d^{10}}{d^2} = d^{10-2} = d^8$ and $\frac{a^3b^6d^2}{ab^4d} = a^2b^2d$ .

When raising a power to another power, use the power of a power rule by multiplying the exponents $(a^m)^n = a^{m \cdot n}$ . For example, $(8^4)^3 = 8^{4 \cdot 3} = 8^{12}$ . With expressions like $(-5w^2z^8)^3$ , apply the rule to each part $(-5)^3 w^{2 \cdot 3} z^{8 \cdot 3} = (-5)^3 w^6 z^{24}$ .

Remember This! Any number (except 0) raised to the power of zero equals 1, so $5^0 = 1$ and $(-4)^0 = 1$ . For negative exponents, flip to the reciprocal $7^{-3} = \frac{1}{7^3}$ and $a^{-5} = \frac{1}{a^5}$ .

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Algebra 1

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418

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Dec 13, 2025

•

1 page

Laws of Exponents: Summary and Review of Key Rules

mia!

@mdotti.ny

Exponent rules make working with powers much simpler! Instead of doing lengthy calculations, these rules give us shortcuts for multiplying, dividing, and raising powers to powers. Mastering these laws will help you solve algebra problems faster and with fewer mistakes.

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Laws of Exponents

When you see expressions with the same base, you can use exponent rules to simplify them quickly. For the product of powers, simply add the exponents when multiplying terms with the same base: $a^m \cdot a^n = a^{m+n}$ . For example, $2^4 \cdot 2^3 = 2^{4+3} = 2^7$ or $(2y)(4y^3) = 8y^4$ .

The quotient of powers rule works by subtracting exponents when dividing terms with the same base: $\frac{a^m}{a^n} = a^{m-n}$ . For instance, $\frac{d^{10}}{d^2} = d^{10-2} = d^8$ and $\frac{a^3b^6d^2}{ab^4d} = a^2b^2d$ .

When raising a power to another power, use the power of a power rule by multiplying the exponents: $(a^m)^n = a^{m \cdot n}$ . For example, $(8^4)^3 = 8^{4 \cdot 3} = 8^{12}$ . With expressions like $(-5w^2z^8)^3$ , apply the rule to each part: $(-5)^3 w^{2 \cdot 3} z^{8 \cdot 3} = (-5)^3 w^6 z^{24}$ .

Remember This! Any number (except 0) raised to the power of zero equals 1, so $5^0 = 1$ and $(-4)^0 = 1$ . For negative exponents, flip to the reciprocal: $7^{-3} = \frac{1}{7^3}$ and $a^{-5} = \frac{1}{a^5}$ .