Question

Simplify this equation please (16a^8/c^12)^1/4

Answer 1

Answer:

$\large\boxed{\left(\dfrac{16a^8}{c^{12}}\right)^\frac{1}{4}=\dfrac{2a^2}{c^3}}$

Step-by-step explanation:

$\left(\dfrac{16a^8}{c^{12}}\right)^\frac{1}{4}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\ \text{and}\ (a^n)^m=a^{nm}\ \text{and}\ (ab)^n=a^nb^n\\\\=\dfrac{(2^4a^8)^\frac{1}{4}}{(c^{12})^\frac{1}{4}}=\dfrac{(2^4)^\frac{1}{4}(a^8)^\frac{1}{4}}{c^{12\cdot\frac{1}{4}}}=\dfrac{2^{4\cdot\frac{1}{4}}\cdot a^{8\cdot\frac{1}{4}}}{c^3}=\dfrac{2^1\cdot a^2}{c^3}=\dfrac{2a^2}{c^3}$

Answer 2

⁴√(16a^8/c^12)

⁴√{((a⁴)(a⁴)(2⁴))/((c⁴)(c⁴)(c⁴)}

2a²/c³

Alternatively,

(⁴√16)(a^(8/4))/(c^(12/4))