Question

find the value of=9^3/2​

Answer 1

Answer:

$= > {9}^{ \frac{3}{2} } \\ \\ = > { ({3}^{2}) }^{ \frac{3}{2} } \\ \\ = > {(3)}^{2 \times \frac{3}{2} } \\ \\ = > {3}^{3} \\ \\ = > 3 \times 3 \times 3 \\ \\ = > 27$

Laws of Exponents:

$Product => {a}^{m} \times {a}^{n}= {a}^{m + n} \\ \\ Quotient => \frac{{a}^{m}}{{a}^{n}} = {a}^{m - n} \\ \\ Power => {({a}^{m})}^{n} = {a}^{m \times n} \\ \\ Inverse => {a}^{-1} = \frac{1}{a} \\ \\ Zero \: Power => {a}^{0} = 1$

Answer 2

Question :

• Find the value of $\sf{9^\frac{4}{2}}$

Solution :

• The given value was :–

:$\implies\sf{9^\frac{3}{2}}$

:$\implies\sf{(3^2)\frac{4}{2}}$

:$\implies\sf{3^2×\frac{4}{2}}$

:$\implies\sf{3^3}$

:$\implies\sf{3×3×3}$

:$\implies\sf{27}$

:$\implies{\underline{\boxed{\green{\sf{Hence,\: the \: answer \: is \: 27}}}}}$

Additionally :

$\bold\orange{Power \: of \: exponents:}$

a n ⋅ b n = (a ⋅ b) n$\implies$32 ⋅ 42 = (3⋅4)

2 = 144$\implies$= a

25 / 23 =$\implies$ 25-3 = 4

a n / b n $\implies$ (a / b) n

43 / 23 $\implies$(4/2)3 = 8

(bn)m$\implies$ bn⋅m

(23)2 $\implies$23⋅2 = 64