enter the correct answer in the box. rewrite the expression $2sqrt4{x^{7}}$ using rational exponents.
enter the correct answer in the box. rewrite the expression $2sqrt4{x^{7}}$ using rational exponents.
Answer
Explanation:
Step1: Recall the radical - exponent rule
The rule for converting a radical $\sqrt[n]{a^m}$ to a rational - exponent is $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. In the given expression $2\sqrt[4]{x^{7}}$, we have $n = 4$ and $m = 7$.
Step2: Apply the rule
Using the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, we can rewrite $\sqrt[4]{x^{7}}$ as $x^{\frac{7}{4}}$. So the expression $2\sqrt[4]{x^{7}}$ can be written as $2x^{\frac{7}{4}}$.
Answer:
$2x^{\frac{7}{4}}$