Exponent rules

Algebra Level 2

$\large 2018 \times 2018^2 \times 2018^3 \times \ldots \times 2018^{63} =?$

2018^{2017}

2018^{2016}

2018^{2018}

2 solutions

Chew-Seong Cheong
Dec 30, 2017

$\begin{aligned} P & = 2018 \times 2018^2 \times 2018^3 \times \cdots \times 2018^{63} \\ &= 2018^{1+2+3+\cdots+63} \\ &= 2018^{\frac{63(64)}2} \\ &= 2018^{2016} \end{aligned}$

Munem Shahriar
Dec 30, 2017

$\dfrac{n(n+1)}{2}$

$\Rightarrow \dfrac{63(63+1)}{2} = \dfrac{4032}{2} = 2016$

Hence $2018^{1+2+3+\ldots +63} = 2018^{2016}$

Exponent rules

2 solutions

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