Use the properties of exponents to simplify the expression. Write with positive exponents.
-$\frac { x ^ { 3 / 2 } \cdot x ^ { - 4 / 7 } } { x ^ { - 2 / 3 } }$

Question

Quizplus · Accepted Answer

To simplify the expression, use the properties of exponents: $x^a \cdot x^b = x^{a+b}$ and $\frac{x^a}{x^b} = x^{a-b}$. First, add the exponents in the numerator: $3/2 + (-4/7) = 21/14 - 8/14 = 13/14$. Then, subtract the exponent in the denominator: $13/14 - (-2/3) = 13/14 + 8/14 = 21/14 = 3/2$. Converting $3/2$ to a denominator of 42 gives $63/42$, which simplifies to $x^{63/42}$. However, the correct calculation should be $3/2 + (-4/7) - (-2/3) = 67/42$, leading to the correct answer $x^{67/42}$.

Use the Properties of Exponents to Simplify the Expression x3/2⋅x−4/7x−2/3\frac { x ^ { 3 / 2 } \cdot x ^ { - 4 / 7 } } { x ^ { - 2 / 3 } }x−2/3x3/2⋅x−4/7​

Use the Properties of Exponents to Simplify the Expression $\frac { x ^ { 3 / 2 } \cdot x ^ { - 4 / 7 } } { x ^ { - 2 / 3 } }$