Question

use positive rational exponents to rewrite the following expression: the square root of x times the 5th root of x

Answer 1

To rewrite the expression using positive rational exponents, we can use the properties of exponents and simplify the expression to x^(7/10).

Step-by-step explanation:

To rewrite the expression using positive rational exponents, we can use the properties of exponents. The square root of x can be written as x^(1/2), and the 5th root of x can be written as x^(1/5). Therefore, the expression can be rewritten as x^(1/2) * x^(1/5).

Using the property of exponents that states when multiplying terms with the same base, we add the exponents, we can simplify the expression to x^(1/2 + 1/5).

Combining the fractions, we get x^(7/10), which is the final expression.

Answer 2

`\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \qquad \sqrt[{ m}]{a^( n)}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ √(x)\cdot \sqrt[5]{x}\implies \sqrt[2]{x^1}\cdot \sqrt[5]{x^1}\implies x^{(1)/(2)}\cdot x^{(1)/(5)}\impliedby \begin{array}{llll} \textit{same base, thus}\\ \textit{add the exponents} \end{array} \\\\\\ x^{(1)/(2)+(1)/(5)}\implies x^{(5+2)/(10)}\implies x^{(7)/(10)}`