Answer:
[tex]8x^8[/tex]
Step-by-step explanation:
Given: [tex]\sqrt{64x^4}[/tex]
This can be written as: [tex]\sqrt{64}[/tex][tex]\sqrt{x^{16} }[/tex]
√64 is the perfect square number.
√64 = [tex]\sqrt{8^2}[/tex]
Here the square and square root will get cancelled, we get
√64 = 8
Now let's simplify [tex]\sqrt{x^{16} } = \sqrt{(x^{8}) ^2}[/tex] = [tex]x^{8}[/tex]
Using the power of power rule for exponents
[tex](a^{m})^n = a^{mn}[/tex]
Therefore, [tex]\sqrt{64x^16} = \sqrt{64} \sqrt{x^{16} } = 8x^8[/tex]
