Question

1. simplify.

$(x^2 y^4)^{\frac{1}{2}}$
$x^4 y^8$
$(xy)^2$
$xy^2$
$x^2 y^2$

1. choose the correct expression.

$sqrt3{25}$
$3^{\frac{1}{25}}$
$25^3$
$25^{\frac{1}{3}}$
$3^{25}$

Explanation:

Question 7

Step 1: Apply exponent rule

Use the power of a product rule \((ab)^n = a^n b^n\) and \((a^m)^n = a^{mn}\). For \((x^2 y^4)^{\frac{1}{2}}\), apply to each term: \(x^{2\times\frac{1}{2}} y^{4\times\frac{1}{2}}\).

Step 2: Simplify exponents

Calculate exponents: \(x^{1} y^{2}\), which is \(xy^2\).

Recall that the \(n\)-th root of a number \(a\) is written as \(a^{\frac{1}{n}}\), so \(\sqrt[3]{25}=25^{\frac{1}{3}}\).

Answer:

\(xy^2\) (the third option, the one with \(xy^2\))

Question 8