Simplify (5×12×4×6) Raised to Power (a+3bx): Complex Base Exponents

Question

Simplify:

$(5\cdot12\cdot4\cdot6)^{a+3bx}$

00:00 Solve

00:04 When there is a power on a product of terms, all terms are raised to that power

00:14 Let's use this formula in our exercise

00:18 Raise each factor to the power

00:34 And this is the solution to the question

Use the power property for a power in parentheses where there is a multiplication of its terms:

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

We apply this law to the problem expression:

$(5\cdot12\cdot4\cdot6)^{a+3bx}=5^{a+3bx}12^{a+3bx}4^{a+3bx}6^{a+3bx}$

When we apply a power to parentheses where its terms are multiplied, we do it separately and keep the multiplication.

Therefore, the correct answer is option d.

$5^{a+3bx}12^{a+3bx}4^{a+3bx}6^{a+3bx}$