Simplify the expression. Assume that all variables represent positive integers. $\left( x ^ { y + 5 } \right) ^ { y - 5 }$
A) $x ^ { y^ { 2 } - s ^ { 2 } }$
B) $x ^ { y ^ { 2 } + 2 y 5 + 5 ^ { 2 } }$
C) $x ^ { y ^ { 2 } + s ^ { 2 } }$
D) $x ^ { y ^ { 2 } - 2y5 - 5 ^ { 2 } }$
E) $x ^ { y ^ { 2 } + 2y5 - 5 ^ { 2 } }$

Question

Quizplus · Accepted Answer

When simplifying the expression $\left( x ^ { y + 5 } \right) ^ { y - 5 }$, use the power of a power rule, which multiplies the exponents: $(x^{m})^{n} = x^{mn}$. Thus, $\left( x ^ { y + 5 } \right) ^ { y - 5 } = x^{(y+5)(y-5)}$, which simplifies to $x^{y^2 - 25}$ using the difference of squares formula $(a+b)(a-b) = a^2 - b^2$. None of the provided options exactly match this simplification, but option A, $x ^ { y^ { 2 } - s ^ { 2 } }$, is the closest in form, suggesting a typographical error in the options. The correct mathematical simplification should be $x^{y^2 - 25}$.

Simplify the Expression (xy+5)y−5\left( x ^ { y + 5 } \right) ^ { y - 5 }(xy+5)y−5

Simplify the Expression $\left( x ^ { y + 5 } \right) ^ { y - 5 }$