Question

which of the following correctly identifies if the statement is true or false and provides the correct justification? the expressions (-x)^y and -x^y have the same value. a) true; both expressions are raising -x to the y power. b) false; the base, -x, is used as a factor y times. the expression -x^y, means the opposite of x^y. c) false; the base x is used as a factor y times in both expressions. d) true; the base, -x, is used as a factor y times. the expression -x^y, means the opposite of x^y.

Explanation:

Step1: Analizar la expresión $(-x)^y$

La expresión $(-x)^y$ significa que el base es $-x$ y se multiplica por sí mismo $y$ veces.

Step2: Analizar la expresión $-x^y$

La expresión $-x^y$ significa el opuesto de $x^y$, es decir, primero se eleva $x$ a la potencia $y$ y luego se cambia el signo. El base en $-x^y$ es $x$, no $-x$.

Answer:

B. false; The base, $-x$, is used as a factor $y$ times. The expression $-x^y$, means the opposite of $x^y$.