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if 16 to the power of x= 1 over 64, what is the value of x

Guest Oct 4, 2017

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Best Answer

+9481

+2

16^x = 1 / 64 Since 2⁴ = 16 and 2⁶ = 64 , we can write this as...

(2⁴)^x = 1 / (2⁶) And (x^a)^b = x^ab, so...

2^4x = 1 / (2⁶) And x^-a = 1 / x^a , so...

2^4x = 2^-6 Now the bases are both equal to 2, so the exponents are equal.

4x = -6 Divide both sides by 4 .

x = -3/2

hectictar Oct 5, 2017

1⁺⁰ Answers

+9481

+2

Best Answer

16^x = 1 / 64 Since 2⁴ = 16 and 2⁶ = 64 , we can write this as...

(2⁴)^x = 1 / (2⁶) And (x^a)^b = x^ab, so...

2^4x = 1 / (2⁶) And x^-a = 1 / x^a , so...

2^4x = 2^-6 Now the bases are both equal to 2, so the exponents are equal.

4x = -6 Divide both sides by 4 .

x = -3/2

hectictar Oct 5, 2017

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