Question

5-30. use the properties of exponents to show that $2 \cdot 3^{x + 1} = 6 \cdot 3^{x}$. step:

Explanation:

Step1: Apply exponent product rule

Recall $a^{m+n}=a^m \cdot a^n$, so $3^{x+1}=3^x \cdot 3^1$.
Substitute into left-hand side:
$2 \cdot 3^{x+1} = 2 \cdot (3^x \cdot 3)$

Step2: Rearrange multiplication order

Use commutative property of multiplication:
$2 \cdot 3 \cdot 3^x$

Step3: Calculate constant product

Compute $2 \cdot 3 = 6$:
$6 \cdot 3^x$

Answer:

By applying exponent and multiplication properties, we show $2 \cdot 3^{x+1} = 6 \cdot 3^x$.