Question 89

What will come in the place of question mark (?) in the following equation ?
$$16^{7.5}\div8^{3.5}\div2^{7.5}$$=?

Solution

As $$16,8,2$$ are all exponents of $$2$$, let us simplify the expression to the powers of 2.

$$16^{7.5} = (2^4)^{7.5} = 2^{30}$$
$$8^{3.5} = (2^3)^{3.5} = 2^{10.5}$$

Hence, the given expression looks like this $$2^{30} \div 2^{10.5} \div 2^{7.5} = 2^{30-10.5-7.5} = 2^{12} = 8^4$$

Hence, the correct answer is option (a)

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