Asked by bianca whiteley on May 20, 2024

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Simplify the expression 13y4/3z−1/528y−2/3z\frac { 13 y ^ { 4 / 3 } z ^ { - 1 / 5 } } { 28 y ^ { - 2 / 3 } z }28y2/3z13y4/3z1/5 .

A) 14y229z6/5\frac { 14 y ^ { 2 } } { 29 z ^ { 6 / 5 } }29z6/514y2
B) 13y228z6/5\frac { 13 y ^ { 2 } } { 28 z ^ { 6 / 5 } }28z6/513y2
C) 13y228z4/5\frac { 13 y ^ { 2 } } { 28 z ^ { 4 / 5 } }28z4/513y2
D) 13y228z1/5\frac { 13 y ^ { 2 } } { 28 z ^ { 1 / 5 } }28z1/513y2
E) y22z6/5\frac { y ^ { 2 } } { 2 z ^ { 6 / 5 } }2z6/5y2

Rational Exponents

Fractional exponents, with the numerator indicating the exponentiation level and the denominator designating the root level of the primary number.

Simplify

The process of making an expression easier to understand by reducing it to its simplest form.

Expression

A combination of symbols and numbers to represent a mathematical operation or quantity.

  • Apply knowledge of exponents and radicals to simplify expressions involving them.
  • Simplify radical expressions involving variables.
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Verified Answer

KW
Kirsten WernerMay 27, 2024
Final Answer :
B
Explanation :
To simplify the expression, combine the terms by adding or subtracting the exponents for like bases. For yyy , add 4/34/34/3 and 2/32/32/3 to get 222 . For zzz , subtract −1/5-1/51/5 from 111 (or add 1/51/51/5 to −1-11 ) to get 6/56/56/5 . The coefficient simplifies directly, remaining 13/2813/2813/28 . Therefore, the simplified expression is 13y228z6/5\frac { 13 y ^ { 2 } } { 28 z ^ { 6 / 5 } }28z6/513y2 .