Solve (a×b×c×4)^7: Multiple Variable Expression with Seventh Power

The power rule for products states that $(a \times b)^n = a^n \times b^n$. When you raise a product to a power, every factor inside the parentheses must be raised to that power.

That's a common mistake! Remember that 4 is also a factor in the product, so it needs the exponent 7 just like the variables. $4^7 = 16,384$ - quite different from just 4!

Not necessarily! The answer $a^7 \times b^7 \times c^7 \times 4^7$ is perfectly acceptable. You can leave $4^7$ as is unless specifically asked to calculate the numerical value.

Huge difference! With multiplication $(a \times b \times c \times 4)^7$, each factor gets the exponent. With addition, you'd need to use the binomial theorem - much more complex!

Yes! Since multiplication is commutative, you can write $4^7 \times a^7 \times b^7 \times c^7$ or any other order. The mathematical meaning stays the same.