Question 75

Select the number that will come in place of the question mark (?) in the mathematical statement.
$$(0.064)^{123} \div 0.16^{47} \times 0.4^{34} \times 0.4^{29} = (0.4)^?$$

Solution

$$(0.064)^{123} \div 0.16^{47} \times 0.4^{34} \times 0.4^{29} = (0.4)^?$$

$$\frac{(0.064)^{123}}{\left(0.16\right)^{47}}\times0.4^{34}\times0.4^{29}=(0.4)^?$$

$$\frac{(0.4)^{3\times\ 123}}{\left(0.4\right)^{2\times47}}\times0.4^{34}\times0.4^{29}=(0.4)^?$$

$$\frac{(0.4)^{369}}{\left(0.4\right)^{94}}\times0.4^{34}\times0.4^{29}=(0.4)^?$$

$$\frac{(0.4)^{369+34+29}}{\left(0.4\right)^{94}}=(0.4)^?$$

$$\frac{(0.4)^{432}}{\left(0.4\right)^{94}}=(0.4)^?$$

$$(0.4)^{432-94}=(0.4)^?$$

$$(0.4)^{338}=(0.4)^?$$
So after comparing the power of 0.4 from both of sides, we can say that 338 will come in place of the question mark.


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