Exponents: Rules and Applications

Front

Product of exponents rule

Back

a^m ⋅ a^n = a^{m+n}

Front

Quotient of exponents rule

Back

a^m / a^n = a^{m-n}

Front

Zero exponent rule

Back

a^0 = 1 (where a ≠ 0)

Front

Power to a power rule

Back

(a^m)^n = a^{m ⋅ n}

Front

Simplify x^3 ⋅ x^4

Back

x^{3+4} = x^7

Front

Simplify y^5 / y^2

Back

y^{5-2} = y^3

Front

Simplify (z^2)^3

Back

z^{2 ⋅ 3} = z^6

Front

b^0

Back

1 (where b ≠ 0)

Front

a^m ⋅ a^0

Back

a^m (since a^0 = 1)

Front

(x^0)^n

Back

1 (since x^0 = 1)