Simplify (2×3×7×9) Raised to Power (ab+3): Complete Expression Solution

While mathematically equivalent, the question asks you to simplify using exponent laws. The distributive form $2^{ab+3} \cdot 3^{ab+3} \cdot 7^{ab+3} \cdot 9^{ab+3}$ shows your understanding of how exponents work with products!

Not necessarily! The problem gives you 9 as a separate factor, so treat it as 9. However, if you want to combine powers of the same base later, you could write $9^{ab+3} = (3^2)^{ab+3} = 3^{2(ab+3)}$.

The same rule applies! $(2 \cdot 3 \cdot 7 \cdot 9)^3 = 2^3 \cdot 3^3 \cdot 7^3 \cdot 9^3$. The distributive property of exponents works with any exponent - variables or numbers.

Think of it as "each factor gets its own copy of the exponent". When you have $(abc)^n$, imagine the exponent n being distributed like gifts - everyone gets one!

For this type of problem, leave them separate! The answer $2^{ab+3} \cdot 3^{ab+3} \cdot 7^{ab+3} \cdot 9^{ab+3}$ clearly shows you applied the exponent law correctly to each factor.