Question

question
which expression is equivalent to \\(\frac{3^0}{3^{-6}}\\)?

answer
\\(3^5\\) \\(3^6\\)
\\(3^{-6}\\) \\(0\\)

Explanation:

Step1: Apply zero exponent rule

Any non-zero number to the power of 0 is 1, so $3^0 = 1$.

Step2: Apply negative exponent rule

A number to a negative exponent is the reciprocal of the number to the positive exponent, so $3^{-6} = \frac{1}{3^6}$.

Step3: Rewrite the original expression

Substitute the above results into $\frac{3^0}{3^{-6}}$:
$\frac{1}{\frac{1}{3^6}} = 1 \times 3^6 = 3^6$
Alternatively, use the quotient rule for exponents: $\frac{a^m}{a^n}=a^{m-n}$, so $\frac{3^0}{3^{-6}}=3^{0-(-6)}=3^{6}$.

Answer:

$3^6$