Inspired by Julian Uy

Algebra Level 2

9 16 x 2 \large \sqrt{ 9 ^ { 16 x^2 } } Which of the following is equal to the above expression?

Inspiration

3 12 x 2 \large 3 ^{12 x^2 } 3 4 x \large 3 ^ { 4 x } 3 12 x \large 3 ^{ 12 x } 3 16 x 2 \large 3 ^ { 16 x^2 }

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Calvin Lin by Calvin Lin

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3 solutions

Nihar Mahajan
Dec 18, 2015

9 16 x 2 = 9 16 x 2 2 = 9 8 x 2 = 3 2 ( 8 x 2 ) = 3 16 x 2 \Large\sqrt{9^{16x^2}} = 9^{\frac{16x^2}{2}} = 9^{8x^2}=3^{2(8x^2)}=3^{16x^2}

Alternatively:

9 16 x 2 = 9 ( 1 2 ) 16 x 2 = ( 9 ) 16 x 2 = 3 16 x 2 \Large\sqrt{9^{16x^2}}= 9^{\left(\frac{1}{2}\right)16x^2} = \left(\sqrt{9}\right)^{16x^2} = 3^{16x^2}

14 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Good approach. There are many ways to write such an exponential. What other examples can you come up with?

Lol only 76% people got it right :P

Aditya Kumar - 5 years, 5 months ago
Aareyan Manzoor
Dec 18, 2015

use rules of exponents . we have that a b = ∣ a b 2 ∣ \sqrt{a^b}=\left|a^{\dfrac{b}{2}}\right| a b 2 = ( a 1 2 ) b = ( a ) b a^{\dfrac{b}{2}}=\left(a^{\dfrac{1}{2}}\right)^b=\left(\sqrt{a}\right)^b we use this 9 16 x 2 = ∣ ( 9 ) 16 x 2 ∣ = 3 16 x 2 \sqrt{9^{16x^2}}=\left|\left(\sqrt{9}\right)^{16x^2}\right|=\boxed{3^{16x^2}}

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Munem Shahriar
Dec 29, 2017

9 16 x 2 = 9 16 x 2 / 2 = ( 3 2 ) 16 x 2 / 2 = 3 16 x 2 \large \sqrt{9^{16 x^2}} = 9^{16x^2/2} = (3^2)^{16x^2/2} = 3^{16x^2}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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