Question

Question 96

Solve the following:

Express as a power of a rational number with negative exponent.
$\left(a\right){\left({\left(\frac{-3}{2}\right)}^{-2}\right)}^{-3}\left(b\right)(2^5÷2^8)\times 2^{-7}$

Answer 1

a) Using laws of exponents,
$(a^m{)}^n=(a{)}^{mxn}and\left(a^{-m}\right)=\frac{1}{a^m}$

$\therefore {\left({\left(\frac{-3}{2}\right)}^{-2}\right)}^{-3}={\left(\frac{-3}{2}\right)}^{-2\times (-3)}$

$={\left(\frac{-3}{2}\right)}^6={\left(\frac{3}{2}\right)}^6$
$={\left(\frac{2}{3}\right)}^{-6}$

b) Using laws of exponents,
$a^m\times a^n=a^{m+n}$

$\therefore (2^5÷2^8)\times 2^{-7}=\left(2^{5-8}\right)\times 2^{-7}=2^{-3}\times 2^{-7}=2^{-3+(-7)}=2^{-3-7}=2^{-10}$