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Question
\frac{710}{50}r^{26.5}
Simplify the expression
\frac{71}{5}r^{26}\sqrt{r}
Evaluate
\frac{710}{50}r^{26.5}
\text{Cancel out the common factor }10
\frac{71}{5}r^{26.5}
Convert the decimal into a fraction
More Steps
Evaluate
26.5
Convert the decimal into a fraction
\frac{265}{10}
Reduce the fraction
\frac{53}{2}
\frac{71}{5}r^{\frac{53}{2}}
\text{Use }{a}^{\frac{m}{n}}=\sqrt[n]{a^{m}}\text{ to transform the expression}
\frac{71}{5}\sqrt{r^{53}}
Solution
More Steps
Evaluate
\sqrt{r^{53}}
Rewrite the exponent as a sum
\sqrt{r^{52+1}}
\text{Use }a^{m+n}=a^m \times a^n\text{ to expand the expression}
\sqrt{r^{52}\times r}
The root of a product is equal to the product of the roots of each factor
\sqrt{r^{52}}\times \sqrt{r}
\text{Reduce the index of the radical and exponent with }2
r^{26}\sqrt{r}
\frac{71}{5}r^{26}\sqrt{r}
Show Solutions
Find the roots
r=0
Evaluate
\frac{710}{50}r^{26.5}
To find the roots of the expression,set the expression equal to 0
\frac{710}{50}r^{26.5}=0
Find the domain
\frac{710}{50}r^{26.5}=0,r\geq 0
Calculate
\frac{710}{50}r^{26.5}=0
\text{Cancel out the common factor }10
\frac{71}{5}r^{26.5}=0
Convert the decimal into a fraction
More Steps
Evaluate
26.5
Convert the decimal into a fraction
\frac{265}{10}
Reduce the fraction
\frac{53}{2}
\frac{71}{5}r^{\frac{53}{2}}=0
Rewrite the expression
r^{\frac{53}{2}}=0
The only way a root could be 0 is when the radicand equals 0
r=0
Check if the solution is in the defined range
r=0,r\geq 0
Solution
r=0
Show Solutions
