Question

Evaluate the following expression
a) (3/2) power 3 × (2/3) power 2​

Answer 1

Answer:

(3/2) power 3 × (2/3) power 2

3×3/2×2×2 × 2×2/3×3

9/8 × 4/9

4/8

1/2

Answer 2

$\frac{3}{2}^{2} *\frac{2}{3} ^{2}$

Method 1

Since the exponents are the same we will apply the following law ⇒

$a^{m} *b^{m} =ab^{m}$

So, now we solve it like this,

$\frac{3}{2}^{2} *\frac{2}{3} ^{2}=(\frac{3}{2}*\frac{2}{3})^{2}$

$\frac{3}{2}^{2} *\frac{2}{3} ^{2}=(\frac{3/3}{2/2}*\frac{2/2}{3/3})^{2}$

$\frac{3}{2}^{2} *\frac{2}{3} ^{2}=(\frac{1}{1}*\frac{1}{1})^{2}$

$\frac{3}{2}^{2} *\frac{2}{3} ^{2}= (1)^{2}$

$\frac{3}{2}^{2} *\frac{2}{3} ^{2} = (1*1)$

$\frac{3}{2}^{2} *\frac{2}{3} ^{2}=1$

Method 2

We substitute the exponents and give the base a whole value and then solve.

So, now we solve it like this,

$\frac{3}{2}^{2} *\frac{2}{3} ^{2}=\frac{3*3}{2*2} *\frac{2*2}{3*3}$

$\frac{3}{2}^{2} *\frac{2}{3} ^{2}=\frac{9}{4}*\frac{4}{9}$

$\frac{3}{2}^{2} *\frac{2}{3} ^{2}=\frac{9/9}{4/4}*\frac{4/4}{9/9}$

$\frac{3}{2}^{2} *\frac{2}{3} ^{2}=\frac{1}{1}*\frac{1}{1}$

$\frac{3}{2}^{2} *\frac{2}{3} ^{2}=\frac{1}{1}$

$\frac{3}{2}^{2} *\frac{2}{3} ^{2}=1$

∴ $\frac{3}{2}^{2} *\frac{2}{3} ^{2}=1$