Question

How do you simplify le="7\sqrt[4]{80pq^{2}r^{8} }" alt="7\sqrt[4]{80pq^{2}r^{8} }" align="absmiddle" class="latex-formula">?

Answer 1

Answer:

$14 ( 5)^{\frac{1}{4}} p^{\frac{1}{4}} q^{\frac{1}{2}} r^{2}$

Step-by-step explanation:

The expression to simplify in this problem is

$7\sqrt[4]{80pq^2r^8}$

Which can be rewritten as

$7(80pq^2r^8)^{\frac{1}{4}}$

Or also as

$7\cdot 80^{\frac{1}{4}} \cdot p^{\frac{1}{4}} \cdot (q^2)^{\frac{1}{4}} \cdot (r^8)^{\frac{1}{4}}$

Now we can apply the following rule for the calculation of the power of a power:

$(a^m)^n = a^{m\cdot n}$

So we get:

$7\cdot 80^{\frac{1}{4}} \cdot p^{\frac{1}{4}} \cdot q^{\frac{1}{2}} \cdot r^{2}$

Which can therefore be rewritten as

$7\cdot (2^4\cdot 5)^{\frac{1}{4}} \cdot p^{\frac{1}{4}} \cdot q^{\frac{1}{2}} \cdot r^{2}$

And so, we get

$7\cdot 2 \cdot ( 5)^{\frac{1}{4}} \cdot p^{\frac{1}{4}} \cdot q^{\frac{1}{2}} \cdot r^{2}$

which can be finally rewritten as

$14 ( 5)^{\frac{1}{4}} p^{\frac{1}{4}} q^{\frac{1}{2}} r^{2}$