Question

simplify the following expression.
$(2c^{7})^{3}(5c^{7}b^{4})^{2}$
show your work here
hint: to add an exponent $(x^{n})$, type \exponent\ or press \^\

Explanation:

Step1: Expand each term via exponent rules

For $(2c^7)^3$: Apply $(ab)^n=a^n b^n$ and $(a^m)^n=a^{m \cdot n}$
$(2c^7)^3 = 2^3 \cdot (c^7)^3 = 8c^{21}$
For $(5c^7b^4)^2$: Apply same exponent rules
$(5c^7b^4)^2 = 5^2 \cdot (c^7)^2 \cdot (b^4)^2 = 25c^{14}b^8$

Step2: Multiply the expanded terms

Multiply coefficients and combine like variables using $a^m \cdot a^n=a^{m+n}$
$8c^{21} \cdot 25c^{14}b^8 = (8 \times 25) \cdot c^{21+14} \cdot b^8$

Step3: Calculate final values

Compute coefficient sum and exponents
$200 \cdot c^{35} \cdot b^8$

Answer:

$200b^8c^{35}$