Question

Find the value of (9/16) ^ - 1/2

Answer 1

4/3

Explanation:

Given:

`\displaystyle \large{\left((9)/(16)\right)^{-(1)/(2)}}`

From the law of exponent:

`\displaystyle \large{a^{-(1)/(2)}=(1)/(√(a))}`

Convert to the form above:

`\displaystyle \large{\left((9)/(16)\right)^{-(1)/(2)}=\frac{1}{\sqrt{(9)/(16)}}}\\\displaystyle \large{\left((9)/(16)\right)^{-(1)/(2)}=(1)/((3)/(4))}\\\displaystyle \large{\left((9)/(16)\right)^{-(1)/(2)}=(4)/(3)}`

Therefore, the solution is 4/3