Question

Please help! Please explain what a integer exponent means and what’s the answer

Answer 1

Answer:

Number 4

Step-by-step explanation:

Using the rule of radicals/ exponents

$\sqrt[n]{x^{m} }$ ⇔ $x^{\frac{m}{n} }$

An integer is a whole number including negative numbers and zero

Z = { ..... - 3, - 2, - 1, 0, 1, 2, 3, .......... }

Consider each in turn using the above rule

(1)

$\sqrt[4]{x^{9} }$ = $x^{\frac{9}{4} }$ ← exponent is not an integer

(2)

$\sqrt[10]{x^{12} }$ = $x^{\frac{12}{10} }$ ← exponent is not an integer

(3)

$\sqrt[12]{x^{18} }$ = $x^{\frac{18}{12} }$ ← exponent is not an integer

(4)

$\sqrt[5]{x^{10} }$ = $x^{\frac{10}{5} }$ = x² ← exponent simplifies to an integer