Write each of the following using positive rational exponents. Match each expression with the corresponding expression.
-$$\frac { 13 } { 11 }$$
$4 y$
A) $4 \sqrt [ 13 ] { y ^ { 11 } }$
B) $4 \sqrt [ 11 ] { y ^ { 13 } }$

Question

Write each of the following using positive rational exponents. Match each expression with the corresponding expression.
-$$\frac { 13 } { 11 }$$
$4 y$ 
A) $4 \sqrt [ 13 ] { y ^ { 11 } }$ 
B) $4 \sqrt [ 11 ] { y ^ { 13 } }$

Quizplus · Accepted Answer

To write $\frac{13}{11}$ with positive rational exponents, we can write it as $\left(\frac{13}{11}\right)^{1}$. To write $4y$ with positive rational exponents, we can write it as $4y^{1}$. Using the rule that $(a^m)^n = a^{mn}$, we can rewrite $\left(\frac{13}{11}\right)^{1}$ as $\left(\frac{13}{11}\right)^{\frac{13}{11}\cdot\frac{1}{13}} = \sqrt[13]{\left(\frac{13}{11}\right)^{13}}$ and we can rewrite $4y^{1}$ as $4\cdot y^{\frac{11}{11}\cdot\frac{13}{11}} = 4\sqrt[11]{y^{13}}$. So the corresponding expression for $\frac{13}{11}$ is B: $4\sqrt[11]{y^{13}}$.

Write Each of the Following Using Positive Rational Exponents 1311\frac { 13 } { 11 }1113​

Write Each of the Following Using Positive Rational Exponents $\frac { 13 } { 11 }$