Question

if a is a real number and m and n are positive integers, then (continued in photo) true or false?

Answer 1

ANSWER

False

EXPLANATION

If

$a$

is a real number and m and n are positive integers, Then,

${a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } = ({ \sqrt[n]{a} })^{m}$

${a}^{ \frac{m}{n} } \ne \sqrt[n]{ {a}^{m} } \ne ({ \sqrt[m]{a} })^{n}$

For instance,

${8}^{ \frac{2}{3} } = \sqrt[3]{ {8}^{2} } = ({ \sqrt[3]{8} })^{2} = 4$

${8}^{ \frac{2}{3} } \ne\sqrt[2]{ {8}^{3} } \ne ({ \sqrt[2]{8} })^{3} \ne4$

Answer 2

Answer: False

Step-by-step explanation: