Answer:
The expression that equivalent to [tex]\frac{12x^{4}}{4x^{16}}[/tex] is 3[tex]x^{4-16}[/tex] ⇒ C
Step-by-step explanation:
Let us revise some rule of exponents
- [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{m+n}[/tex]
- [tex]\frac{a^{m}}{a^{n}}[/tex] = [tex]a^{m-n}[/tex]
- [tex](a^{m})^{n}[/tex] = [tex]a^{mn}[/tex]
Let us solve the question
∵ The expression is [tex]\frac{12x^{4}}{4x^{16}}[/tex]
→ Simplify the fraction 12/4 first
∵ 12/4 = 3
∴ [tex]\frac{12x^{4}}{4x^{16}}[/tex] = 3 ( [tex]\frac{x^{4}}{x^{16}}[/tex])
→ By using the second rule above to simplify the variable
∵ [tex]\frac{x^{4}}{x^{16}}[/tex] = [tex]x^{4-16}[/tex]
∴ [tex]\frac{12x^{4}}{4x^{16}}[/tex] = 3[tex]x^{4-16}[/tex]
∴ The expression that equivalent to [tex]\frac{12x^{4}}{4x^{16}}[/tex] is 3[tex]x^{4-16}[/tex]
