Zero Law
$(a)^0 = 1$
$2^0 = 1$,$(-5)^0=1$
Product
$a^m × a^n = a ^{m+n}$
$4^5 + 4^3 = 4^{5+3} = 4^8$
Quotient
${a^m} / {a^n} = a ^{m-n}$
$4^5 / 4^3 = 4^{5-3} = 4^2$
Power of a power
$(a^m)^n = a^{mn}$
$(4^5)^3 = 4^{5×3} = 4^{15}$
Power of a product
$(ab)^n = a^n b^n$
$(2×3)^5 = 2^5 × 3^5$
Power of a quotient
$(a / b)^n = a^n / b^n$
$(2 / 3)^5 = 2^5 / 3^5$
Negative Exponent
$a^{-n} = 1 / a^n$
$2^{-5} = 1 / 2^5$
Negative Exponent of a fraction
$(a / b)^{-n} = (b / a)^{n} = b^n / a^n$
$(2 / 3)^{-5} = (3 / 2)^{5} = 3^5 / 2^5$
Fractional / Rational Exponent $m/n$
$a^{m/n} = √^na^m $
or
$(√^na)^m$
$8^{5/3} = √^3 8 ^5 $
or
$(√^3 8)^5$
Fractional / Rational Exponent $1/2$
$a^{1/2} = √^2 a$
or just
$√a$
$4^{1/2} = √^2 4$
or just
$√4$
Fractional / Rational Exponent $1/3$
$a^{1/3} = √^3 a$
$8^{1/3} = √^3 8$
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