Asked by Ghadeer NasEr on May 17, 2024
Verified
Simplify the expression. Assume that all variables represent positive integers. (xy+5) y−5\left( x ^ { y + 5 } \right) ^ { y - 5 }(xy+5) y−5
A) xy2−s2x ^ { y^ { 2 } - s ^ { 2 } }xy2−s2
B) xy2+2y5+52x ^ { y ^ { 2 } + 2 y 5 + 5 ^ { 2 } }xy2+2y5+52
C) xy2+s2x ^ { y ^ { 2 } + s ^ { 2 } }xy2+s2
D) xy2−2y5−52x ^ { y ^ { 2 } - 2y5 - 5 ^ { 2 } }xy2−2y5−52
E) xy2+2y5−52x ^ { y ^ { 2 } + 2y5 - 5 ^ { 2 } }xy2+2y5−52
Expression Simplification
The process of making an algebraic expression more manageable by combining like terms and applying mathematical operations.
- Simplify expressions involving powers and exponents.
Verified Answer
JB
Jeanette BrouillardMay 23, 2024
Final Answer :
A
Explanation :
When simplifying the expression (xy+5)y−5\left( x ^ { y + 5 } \right) ^ { y - 5 }(xy+5)y−5 , use the power of a power rule, which multiplies the exponents: (xm)n=xmn(x^{m})^{n} = x^{mn}(xm)n=xmn . Thus, (xy+5)y−5=x(y+5)(y−5)\left( x ^ { y + 5 } \right) ^ { y - 5 } = x^{(y+5)(y-5)}(xy+5)y−5=x(y+5)(y−5) , which simplifies to xy2−25x^{y^2 - 25}xy2−25 using the difference of squares formula (a+b)(a−b)=a2−b2(a+b)(a-b) = a^2 - b^2(a+b)(a−b)=a2−b2 . None of the provided options exactly match this simplification, but option A, xy2−s2x ^ { y^ { 2 } - s ^ { 2 } }xy2−s2 , is the closest in form, suggesting a typographical error in the options. The correct mathematical simplification should be xy2−25x^{y^2 - 25}xy2−25 .
Learning Objectives
- Simplify expressions involving powers and exponents.
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