Question

Question 84

In the following question, state whether the given statements are true (T) or false (F).

The exponential form for
$(-2{)}^4\times {\left(\frac{5}{2}\right)}^{4}is(5^4).$

Answer 1

True:

Using law of exponents,
$a^m÷a^n=(a{)}^{m-n}and{\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$

$\therefore (-2{)}^4\times {\left(\frac{5}{2}\right)}^4=(-1{)}^4(2{)}^4\times \frac{(5{)}^4}{(2{)}^4}=(2{)}^{4-4}\times 5^4=2^0\times 5^4=5^4$