How would I simplify the square root of (x+5)^16?
How would I simplify the square root of (x+5)^16?
the answer is (x+5)⁸
here's the proof
recall that
\(\sqrt{x} =x^ \frac{1}{2}\) and
\((x^m)^n=x^{mn}\)
therefore
\(\sqrt{(x+5)^{16}} =((x+5)^{16})^ \frac{1}{2}=(x+5)^{(16)( \frac{1}{2})}=(x+5)^8\)
the simplified form is (x+5)⁸