Question

write an equivalent expression with positive exponents only.
$x^4y^{-2}$
which choice is correct?
a. $xy^2$
b. $\frac{x^4}{y^2}$
c. $\frac{1}{x^4y^2}$
d. $(xy)^2$

Explanation:

Step1: Recall negative exponent rule

The rule for negative exponents is \( a^{-n}=\frac{1}{a^{n}} \) (where \( a
eq0 \) and \( n \) is a positive integer). For the term \( y^{-2} \), applying this rule, we get \( y^{-2}=\frac{1}{y^{2}} \).

Step2: Rewrite the original expression

The original expression is \( x^{4}y^{-2} \). Substituting \( y^{-2}=\frac{1}{y^{2}} \) into the expression, we have \( x^{4}\times\frac{1}{y^{2}}=\frac{x^{4}}{y^{2}} \).

Answer:

B. \(\frac{x^{4}}{y^{2}}\)