Question

rewrite the expression $12^{0} \cdot 5^{-2}$ using only positive exponents.
rewrite $5^{-2}$ using a positive exponent.
$12^{0} \cdot 5^{-2} = 1 \cdot 5^{-2}
= 5^{-2}
= ?$
$-5^{2}$
$-\frac{1}{5^{2}}$
$\frac{1}{5^{2}}$
$5^{2}$

Explanation:

Step1: Apply zero exponent rule

$12^0 = 1$, so $12^0 \cdot 5^{-2} = 1 \cdot 5^{-2} = 5^{-2}$

Step2: Apply negative exponent rule

For any non-zero $a$ and integer $n$, $a^{-n} = \frac{1}{a^n}$. So $5^{-2} = \frac{1}{5^2}$

Answer:

$\frac{1}{5^2}$ (corresponding to the option $\boldsymbol{\frac{1}{5^2}}$)