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

Question

Simplify:

$(2\cdot3\cdot7\cdot9)^{ab+3}$

00:00 Simplify the expression

00:03 When there is a power on a product of terms, all terms are raised to that power

00:13 We will use this formula in our exercise

00:17 Raise each factor to the power

00:32 And this is the solution to the question

We begin by using the distributive law of exponents.

$(x\cdot y)^n=x^n\cdot y^n$

We apply this property to the given problem :

$(2\cdot3\cdot7\cdot9)^{ab+3} =2^{ab+3}3^{ab+3}7^{ab+3}9^{ab+3}$

When we apply the power of parentheses to each of the terms of the product inside the parentheses separately and maintain the multiplication.

Therefore, the correct answer is option a.

$2^{ab+3}3^{ab+3}7^{ab+3}9^{ab+3}$