tyna simplified the expression $\frac{3x^{3}}{12x^{-2}}$ to $\frac{x}{4}$. what was tynas mistake?\nshe…
tyna simplified the expression $\frac{3x^{3}}{12x^{-2}}$ to $\frac{x}{4}$. what was tynas mistake?\nshe divided the coefficients incorrectly.\nshe added the exponents instead of subtracting them.\nshe divided the coefficients instead of subtracting them.\nshe subtracted the exponents instead of dividing them.
Answer
Explanation:
Step1: Simplify the given expression
When dividing two terms with the same base ($x$) in the form $\frac{a x^{m}}{b x^{n}}$, we use the rule $\frac{a}{b}x^{m - n}$. For the expression $\frac{3x^{3}}{12x^{- 2}}$, first divide the coefficients: $\frac{3}{12}=\frac{1}{4}$, and then subtract the exponents of $x$: $x^{3-(-2)}=x^{3 + 2}=x^{5}$. So the correct simplified form is $\frac{1}{4}x^{5}$.
Step2: Analyze Tyna's result
Tyna got $\frac{x}{4}$, which means she correctly divided the coefficients ($\frac{3}{12}=\frac{1}{4}$), but she made a mistake with the exponents. She should have subtracted the exponents of $x$ ($3-(-2)$) instead of some other incorrect operation.
Answer:
She added the exponents instead of subtracting them.