Question

question
fully simplify using only positive exponents.
\\(\dfrac{(10c^4)(2c^3)^2}{8c^5}\\)

Explanation:

Step1: Expand the squared term

Use exponent rule $(x^a)^b=x^{a\cdot b}$:
$(2c^3)^2=2^2\cdot c^{3\cdot2}=4c^6$

Step2: Multiply numerator terms

Multiply coefficients and add exponents:
$(10c^4)(4c^6)=10\cdot4\cdot c^{4+6}=40c^{10}$

Step3: Divide by denominator

Divide coefficients and subtract exponents:
$\frac{40c^{10}}{8c^5}=\frac{40}{8}\cdot c^{10-5}=5c^5$

Answer:

$5c^5$