Question

simplify 27 2\3 x 125 1\3

Answer 1

Answer:

27⅔=(3×3×3)⅔=(3³)⅔=3²=9

125⅓=(5×5×5)⅓=(5)³)⅓=5¹=5

27⅔×125⅓=9×5=45

Answer 2

Question :-

Simplify : $27^\frac{2}{3} \times 125^\frac{1}{3}$

$\begin {gathered} \end {gathered}$

Solution :-

We have :

$\begin {aligned} \bold {27^\frac{2}{3} \times 125^\frac{1}{3}} & = (3^3)^\frac{2}{3} \times (5^3)^\frac{1}{3}\\\\& \Rightarrow 3^{3 \times \frac{2}{3}} \times 5^{3\times \frac{1}{3}}\\\\& \Rightarrow 3^2 \times 5^1 \implies 9 \times 5 = \bold {45} \end {aligned}$

$\begin {gathered} \end {gathered}$

Laws Used :-

i. $a^\frac{1}{n} \Rightarrow (a^n)^\frac{1}{n} = a$

i. $(a^m)^n = a^{m \times n}$

$\begin {gathered} \end {gathered}$

Additional Information :-

Some more Laws of Exponents :-

i. $a^m \times a^nn = a^{m + n}$

ii. $\dfrac{a^m}{a^n} = a^{m - n}$

iii. $a^m \times b^m = (a \times b)^m$

iv. $\Big (\dfrac{a}{b}\Big )^m = \dfrac{a^m}{b^m}$

v. $a^0 = 1$

vi. $\sqrt[n]{a} = a^\frac{1}{n}$