Simplify ((12^5)/(12^-5))^0

${(\frac{12^{5}}{12^{- 5}})}^{0}$

Step 1

Move $12^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(12^{5} \cdot 12^{5})}^{0}$

Step 2

Multiply $12^{5}$ by $12^{5}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(12^{5 + 5})}^{0}$

Add $5$ and $5$ .

${(12^{10})}^{0}$

Step 3

Multiply the exponents in ${(12^{10})}^{0}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$12^{10 \cdot 0}$

Multiply $10$ by $0$ .

$12^{0}$

Step 4

Anything raised to $0$ is $1$ .

$1$