Question

rewrite using a single positive exponent.\\((5^{-3})^{4}\\)

Explanation:

Step1: Apply power of a power rule

When raising a power to a power, multiply exponents: $(a^m)^n = a^{m \times n}$.
So, $(5^{-3})^4 = 5^{-3 \times 4}$

Step2: Calculate the new exponent

Compute the product of the exponents:
$5^{-3 \times 4} = 5^{-12}$

Step3: Convert to positive exponent

Use the rule $a^{-k} = \frac{1}{a^k}$ to rewrite with a positive exponent:
$5^{-12} = \frac{1}{5^{12}}$

Answer:

$\frac{1}{5^{12}}$