Question

evaluate (2/3)^8 x (6/4)^3​

Answer 1

Solution:-

$\implies \: (\frac{2}{3} ) {}^{8} \times (\cancel{\frac{6}{4}}) {}^{3} \\ \\ \\ \implies \: ( \frac{2}{3} ) {}^{8} \times ( \frac{3}{2} ) {}^{3} \\ \\ \\ \implies \: \: (\frac{2}{3} ) {}^{8} \times (\frac{2}{3} ) {}^{ - 3} \\ \\ \\ \implies \: ( \frac{2}{3}) {}^{8 - 3} \\ \\ \\ \implies \: (\frac{2}{3} ) {}^{5} \\ \\ \\ \implies \: \frac{32}{243}$

formula uses

$\implies \pink{ (\frac{a}{b}) {}^{m} = ( \frac{b}{a} ) {}^{ - m} } \\ \\ \\ \implies \pink{a {}^{m} .a {}^{n} = a {}^{m + n} }$

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Answer 2

• We have to evaluate the above expression by using the given data.

        Given data:- $(\frac{2}{3} )^{8} \times (\frac{6}{4} )^{3} .$

        To find:- Value of given expression=?

        Solution:-

• Multiplication is denoted by the symbol(x).

• Multiplication is a method to get the product by multiplying two or more values.

• There are six properties of multiplication is given below:-

1. Closure property.
2. Commutative property.
3. Associative property.
4. Distributive property.
5. Identity property.
6. Zero property.

       Therefore we get,

         $(\frac{2}{3} )^{8} \times (\frac{6}{4} )^{3} \\\\\Rightarrow\left(\frac{2}{3}\right)^{8} \times\left(\frac{3}{2}\right)^{3} \\\\\Rightarrow\left(\frac{2}{3}\right)^{8} \times\left(\frac{2}{3}\right)^{-3} \\\\\Rightarrow\left(\frac{2}{3}\right)^{8-3} \\\\\Rightarrow\left(\frac{2}{3}\right)^{5} \\\\\Rightarrow \frac{32}{243}\end{array}$

       Hence we will get the value $\frac{32}{243}.$