Question
Using laws of exponent, simplify and write the answer in exponential form: $\left(2^{20} \div 2^{15}\right) \times 2^3$
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Answer
By the law of exponents we have, $x^m \div x^n=x^{m-n}$
By applying this law, we have $\left(2^{20} \div 2^{15}\right)=2^{20-15}=2^5$
$\left(2^{20} \div 2^{15}\right) \times 2^3=2^5 \times 2^3$
Again, we have $x^m \times x^n=x^{m+n}$
By applying this we have, $2^5 \times 2^3=2^{5+3}=2^8$ Hence, $\left(2^{20} \div 2^{15}\right) \times 2^3=2^8$
By applying this law, we have $\left(2^{20} \div 2^{15}\right)=2^{20-15}=2^5$
$\left(2^{20} \div 2^{15}\right) \times 2^3=2^5 \times 2^3$
Again, we have $x^m \times x^n=x^{m+n}$
By applying this we have, $2^5 \times 2^3=2^{5+3}=2^8$ Hence, $\left(2^{20} \div 2^{15}\right) \times 2^3=2^8$
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