How to combine $5*3^{(x+1)}$

Question

I came across the following equality: $$\frac{2^x}{5*3^{(x+1)}}=\frac1{15}\left(\frac23\right)^x$$ Why is this?

More specifically, what I don't understand is how to combine the $5*3^{(x+1)}$.

score 2 · Answer 1 · answered Dec 27 '19 at 03:53

2

$3^{x+1}=3\times3^x$ so

$$\frac{2^x}{5\times3^{x+1}}= \frac{2^x}{5\times(3\times3^x)}= \frac{2^x}{(5\times3)\times3^x}=\frac1{15}\left(\frac23\right)^x$$

answered Dec 27 '19 at 03:53

J. W. Tanner

score 2 · Accepted Answer · answered Dec 27 '19 at 03:54

2

Use the law of exponents $$3^{x+y}=3^x×3^y$$ So, $$5×3^{x+1}=5×3×3^x$$

answered Dec 27 '19 at 03:54

Martund

2 Answers2