Verify by numerical sua a. \( \left(2 y^{4}\right)^{3} \)

To verify \( \left(2 y^{4}\right)^{3} \) numerically, let's calculate it step by step. First, we raise the coefficient and the variable power separately. The coefficient \( 2 \) raised to the power of \( 3 \) is \( 2^3 = 8 \). Next, we take \( y^{4} \) raised to the power of \( 3 \): \[ \left( y^{4} \right)^{3} = y^{4 \times 3} = y^{12}. \] Now we combine these results: \[ \left(2 y^{4}\right)^{3} = 8 y^{12}. \] So, we can conclude that \( \left(2 y^{4}\right)^{3} = 8 y^{12} \) is verified. Now, let's have some fun! To get a taste of the past, can you imagine how mathematicians in ancient times might have computed powers without modern tools? They relied on sheer ingenuity and manual calculations. Speaking of calculations, a common mistake when dealing with powers is forgetting to apply the exponent to both the number and the variable. Always double-check to make sure every part gets the love it deserves!