Evaluate the Expression: Expanding (6×b)⁴

Because of the Power of a Product Rule! When you have $(ab)^n$, the exponent n distributes to each factor, giving you $a^n \times b^n$. Think of it as multiplying the entire expression by itself 4 times.

Huge difference! $6^4 \times b^4 = 1296b^4$ while $6 \times b^4 = 6b^4$. The first correctly applies the power rule, but the second misses the exponent on 6, making it much smaller.

Not necessarily! The expression $6^4 \times b^4$ is already simplified in its current form. You could calculate $6^4 = 1296$ to write $1296b^4$, but both forms are correct.

Absolutely! For example, $(2 \times x \times y)^3 = 2^3 \times x^3 \times y^3$. The exponent distributes to every single factor inside the parentheses, no matter how many there are.

Great question! A negative sign acts like $-1$, so $(-6b)^4 = (-1)^4 \times 6^4 \times b^4 = 1 \times 6^4 \times b^4 = 6^4b^4$. Since $(-1)^4 = 1$, the result is positive!