To determine the correct product of the given fractions, let's proceed step-by-step.
### Step 1: Identify the fractions
The fractions provided are:
- [tex]\( \frac{8}{15} \)[/tex]
- [tex]\( \frac{6}{5} \)[/tex]
- [tex]\( \frac{1}{3} \)[/tex]
### Step 2: Multiply the numerators
The numerators of the three fractions are [tex]\( 8 \)[/tex], [tex]\( 6 \)[/tex], and [tex]\( 1 \)[/tex].
Multiplying these together:
[tex]\[ 8 \times 6 \times 1 = 48 \][/tex]
### Step 3: Multiply the denominators
The denominators of the three fractions are [tex]\( 15 \)[/tex], [tex]\( 5 \)[/tex], and [tex]\( 3 \)[/tex].
Multiplying these together:
[tex]\[ 15 \times 5 \times 3 = 225 \][/tex]
### Step 4: Form the resulting fraction
The product of the fractions will thus be:
[tex]\[ \frac{48}{225} \][/tex]
### Step 5: Analyze the options given
From the options provided:
A. [tex]\( \frac{16}{75} \)[/tex]
B. [tex]\( \frac{48}{15} \)[/tex]
C. [tex]\( \frac{16}{15} \)[/tex]
D. [tex]\( \frac{48}{30} \)[/tex]
None of these options directly match the fraction we derived, which is [tex]\( \frac{48}{225} \)[/tex]. If the problem requires simplification that fits a specific context (like matching to provided simplified options), we acknowledge that from our calculations, no provided options are equivalent to [tex]\( \frac{48}{225} \)[/tex].
Thus, with the fractions as computed, none of the provided options here are accurate based on the product of [tex]\( \frac{8}{15} \)[/tex], [tex]\( \frac{6}{5} \)[/tex], and [tex]\( \frac{1}{3} \)[/tex].
