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Question
x^{-1}\times x^{-\frac{3}{5}}
Simplify the expression
\frac{\sqrt[5]{x^{2}}}{x^{2}}
Evaluate
x^{-1}\times x^{-\frac{3}{5}}
\text{Use the product rule }a^{n}\times a^{m}=a^{n+m}\text{ to simplify the expression}
x^{-1-\frac{3}{5}}
Subtract the numbers
More Steps
Evaluate
-1-\frac{3}{5}
Reduce fractions to a common denominator
-\frac{5}{5}-\frac{3}{5}
Write all numerators above the common denominator
\frac{-5-3}{5}
Subtract the numbers
\frac{-8}{5}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
-\frac{8}{5}
x^{-\frac{8}{5}}
\text{Express with a positive exponent using }a^{-n}=\frac{1}{a^n}
\frac{1}{x^{\frac{8}{5}}}
Transform the expression
More Steps
Evaluate
x^{\frac{8}{5}}
\text{Use }{a}^{\frac{m}{n}}=\sqrt[n]{a^{m}}\text{ to transform the expression}
\sqrt[5]{x^{8}}
Rewrite the exponent as a sum
\sqrt[5]{x^{5+3}}
\text{Use }a^{m+n}=a^m \times a^n\text{ to expand the expression}
\sqrt[5]{x^{5}\times x^{3}}
The root of a product is equal to the product of the roots of each factor
\sqrt[5]{x^{5}}\times \sqrt[5]{x^{3}}
\text{Reduce the index of the radical and exponent with }5
x\sqrt[5]{x^{3}}
\frac{1}{x\sqrt[5]{x^{3}}}
Multiply by the Conjugate
\frac{1\times \sqrt[5]{x^{2}}}{x\sqrt[5]{x^{3}}\times \sqrt[5]{x^{2}}}
Calculate
\frac{1\times \sqrt[5]{x^{2}}}{x\times x}
Any expression multiplied by 1 remains the same
\frac{\sqrt[5]{x^{2}}}{x\times x}
Solution
\frac{\sqrt[5]{x^{2}}}{x^{2}}
Show Solutions
Find the roots
x \in \varnothing
Evaluate
x^{-1}\times x^{-\frac{3}{5}}
To find the roots of the expression,set the expression equal to 0
x^{-1}\times x^{-\frac{3}{5}}=0
Find the domain
x^{-1}\times x^{-\frac{3}{5}}=0,x\neq 0
Calculate
x^{-1}\times x^{-\frac{3}{5}}=0
Multiply the terms
More Steps
Evaluate
x^{-1}\times x^{-\frac{3}{5}}
\text{Use the product rule }a^{n}\times a^{m}=a^{n+m}\text{ to simplify the expression}
x^{-1-\frac{3}{5}}
Subtract the numbers
More Steps
Evaluate
-1-\frac{3}{5}
Reduce fractions to a common denominator
-\frac{5}{5}-\frac{3}{5}
Write all numerators above the common denominator
\frac{-5-3}{5}
Subtract the numbers
\frac{-8}{5}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
-\frac{8}{5}
x^{-\frac{8}{5}}
x^{-\frac{8}{5}}=0
Rewrite the expression
\frac{1}{x^{\frac{8}{5}}}=0
Cross multiply
1=x^{\frac{8}{5}}\times 0
Simplify the equation
1=0
Solution
x \in \varnothing
Show Solutions
