Find the product. Assume variables represent positive real numbers.
-$$6 x ^ { 6 / 5 } \left( x ^ { 11 / 5 } - 7 x \right)$$
A) $\frac { 6 } { x ^ { 17 / 5 } } - \frac { 42 } { x ^ { 11 / 5 } }$

B) $\frac { 6 } { x ^ { 17 / 5 } } - 42 x ^ { 11 / 5 }$

C) $6 x ^ { 17 / 5 } - \frac { 42 } { x ^ { 11 / 5 } }$

D) $6 x ^ { 17 / 5 } - 42 x ^ { 11 / 5 }$

Question

Find the product. Assume variables represent positive real numbers.
-$$6 x ^ { 6 / 5 } \left( x ^ { 11 / 5 } - 7 x \right)$$
A) $\frac { 6 } { x ^ { 17 / 5 } } - \frac { 42 } { x ^ { 11 / 5 } }$

B) $\frac { 6 } { x ^ { 17 / 5 } } - 42 x ^ { 11 / 5 }$

C) $6 x ^ { 17 / 5 } - \frac { 42 } { x ^ { 11 / 5 } }$

D) $6 x ^ { 17 / 5 } - 42 x ^ { 11 / 5 }$

Quizplus · Accepted Answer

To find the product, apply the distributive property $a(b + c) = ab + ac$. For $6x^{6/5}(x^{11/5} - 7x)$, distribute $6x^{6/5}$ across the parentheses. Use the rule for multiplying powers with the same base: $a^m \cdot a^n = a^{m+n}$. For $x^{6/5} \cdot x^{11/5}$, add the exponents: $6/5 + 11/5 = 17/5$, resulting in $6x^{17/5}$. For the second term, $7x$ is equivalent to $7x^{5/5}$ to have a common base with the first term. Thus, $6x^{6/5} \cdot 7x^{5/5} = 42x^{(6/5 + 5/5)} = 42x^{11/5}$. Therefore, the product is $6x^{17/5} - 42x^{11/5}$.

Find the Product 6x6/5(x11/5−7x)6 x ^ { 6 / 5 } \left( x ^ { 11 / 5 } - 7 x \right)6x6/5(x11/5−7x)

Find the Product $6 x ^ { 6 / 5 } \left( x ^ { 11 / 5 } - 7 x \right)$