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What will come in place of the question mark (?) in the following questions ?
Question 113
$$(0.0729 \div 0.1)^{3}\div (0.081 \times 10)^{5}$$ $$\times (0.3 \times 3)^{5}=(0.9)^{?+3}$$
Solution
Expression : $$(0.0729 \div 0.1)^{3}\div (0.081 \times 10)^{5}$$ $$\times (0.3 \times 3)^{5}=(0.9)^{?+3}$$
=> $$(\frac{0.0729}{0.1})^3 \div (0.81)^5 \times (0.9)^5 = (0.9)^{x + 3}$$
=> $$(0.729)^3 \times \frac{1}{(0.9^2)^5} \times (0.9)^5 = (0.9)^{x + 3}$$
=> $$(0.9^3)^3 \times (0.9)^{5 - 10} = (0.9)^{x + 3}$$
=> $$(0.9)^{9 - 5} = (0.9)^{x + 3}$$
Comparing powers on both sides
=> $$x + 3 = 4$$
=> $$x = 4 - 3 = 1$$
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