Question

simplify the following expression. if the answer contains exponents, all exponents sh\\(\frac{(s^{8})^{2}(s^{2})^{3}}{(s^{2})^{6}} = \\)\
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Explanation:

Step1: Apply power of a power rule

For each term, multiply exponents:
$(s^8)^2 = s^{8\times2}=s^{16}$, $(s^2)^3=s^{2\times3}=s^6$, $(s^2)^6=s^{2\times6}=s^{12}$
Expression becomes: $\frac{s^{16}s^{6}}{s^{12}}$

Step2: Apply product of powers rule

Add exponents in numerator:
$s^{16}s^{6}=s^{16+6}=s^{22}$
Expression becomes: $\frac{s^{22}}{s^{12}}$

Step3: Apply quotient of powers rule

Subtract exponents:
$s^{22-12}=s^{10}$

Answer:

$s^{10}$