Add or subtract. Assume all variables represent nonnegative real numbers.
-$$8 \sqrt [ 5 ] { \mathrm { m } ^ { 11 } \mathrm { p } ^ { 7 } } - 2 \mathrm {~m} ^ { 2 } \mathrm { p } \sqrt [ 5 ] { \mathrm { mp } ^ { 2 } }$$
A) $10 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$
B) $6 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$
C) 6
D) Cannot simplify

Question

Quizplus · Accepted Answer

To simplify the given expression, we first express both terms under the fifth root in a similar manner to combine them. The first term is already in a simplified form, while the second term can be rewritten by factoring out $m^2p$ and adjusting the exponent inside the root to match the first term. This results in both terms having a common factor, allowing them to be combined into $6 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$.

Add or Subtract 8m11p75−2 m2pmp258 \sqrt [ 5 ] { \mathrm { m } ^ { 11 } \mathrm { p } ^ { 7 } } - 2 \mathrm {~m} ^ { 2 } \mathrm { p } \sqrt [ 5 ] { \mathrm { mp } ^ { 2 } }85m11p7​−2 m2p5mp2​

Add or Subtract $8 \sqrt [ 5 ] { \mathrm { m } ^ { 11 } \mathrm { p } ^ { 7 } } - 2 \mathrm {~m} ^ { 2 } \mathrm { p } \sqrt [ 5 ] { \mathrm { mp } ^ { 2 } }$