Question

which expression is equivalent to $3^{0} \cdot 3^{-8}$?
$\frac{3^{0}}{3^{9}}$, $3^{0}$, $(3^{9})^{-9}$, $\frac{1}{3^{8}}$

Explanation:

Step1: Apply exponent product rule

When multiplying exponents with the same base, add the exponents: $a^m \cdot a^n = a^{m+n}$.
$3^0 \cdot 3^{-8} = 3^{0 + (-8)} = 3^{-8}$

Step2: Rewrite negative exponent

A negative exponent means the reciprocal: $a^{-n} = \frac{1}{a^n}$.
$3^{-8} = \frac{1}{3^8}$

Step3: Verify other options

• $\frac{3^0}{3^9} = 3^{0-9}=3^{-9}

eq 3^{-8}$

• $3^0 = 1

eq 3^{-8}$

• $(3^9)^{-9}=3^{9 \times (-9)}=3^{-81}

eq 3^{-8}$

Answer:

$\frac{1}{3^8}$