Use the properties of exponents to simplify the expression. Write with positive exponents.
-$\frac { \left( 2 x ^ { 1 / 4 } \right) ^ { 7 } } { x ^ { - 2 / 7 } }$
A) $128 x ^ { 41 / 28 }$
B) $128 x ^ { 57 / 28 }$
C) $2 x ^ { 41 / 28 }$
D) $2 x ^ { 57 / 28 }$

Question

Quizplus · Accepted Answer

First, simplify the numerator using the power of a power rule, which states that $(a^m)^n = a^{mn}$. Thus, $(2x^{1/4})^7 = 2^7x^{7/4}$. Since $2^7 = 128$, the numerator becomes $128x^{7/4}$. For the denominator, since it's $x^{-2/7}$, you can bring it to the numerator by changing the sign of the exponent to get $x^{2/7}$. Combining the exponents of $x$ in the numerator by adding them (since $x^{m} \cdot x^{n} = x^{m+n}$), you get $x^{(7/4) + (2/7)}$. Finding a common denominator (28) and adding the fractions gives $x^{(49/28) + (8/28)} = x^{57/28}$. Therefore, the simplified expression is $128x^{57/28}$.

Use the Properties of Exponents to Simplify the Expression (2x1/4)7x−2/7\frac { \left( 2 x ^ { 1 / 4 } \right) ^ { 7 } } { x ^ { - 2 / 7 } }x−2/7(2x1/4)7​

Use the Properties of Exponents to Simplify the Expression $\frac { \left( 2 x ^ { 1 / 4 } \right) ^ { 7 } } { x ^ { - 2 / 7 } }$