Answer
$\frac{j^{32}}{32k^{26}}$
Work Step by Step
When we raise a power to a power, we multiply the powers together and keep the base. Let's multiply the exponent of each term by the exponent outside of the parentheses:
$2^{-5}j^{(2)(-5)}k^{(4)(-5)}k^{(-1)(6)}j^{(7)(6)}$
Multiply the exponents:
$2^{-5}j^{-10}k^{-20}k^{-6}j^{42}$
Simplify the expression by moving bases with negative exponents into the denominator:
$\frac{j^{42}}{32j^{10}k^{20}k^{6}}$
We have $j$ terms in both the numerator and denominator, so we subtract the exponents and keep the base:
$\frac{j^{32}}{32k^{20}k^{6}}$
When multiplying exponents with the same base, we add the exponents and keep the same base:
$\frac{j^{32}}{32k^{26}}$
