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If 16 to the power of x equals 1/64 find the value of x

User Ya Xiao
by
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1 Answer

3 votes

Answer:


\sf x = (-3)/(2)

Explanation:

Exponents:

Prime factorize 16 and 64 and write in exponent form.


\sf \boxed{\bf (1)/(a^m)=a^(-m)}\\\\\\\boxed{\bf (a^m)^n =a^(m*n)}


\sf 16^x = (1)/(64)\\\\ (4^2)^x= 64^(-1)\\\\ (4^2)^x = (4^3)^(-1)\\\\ 4^(2x)=4^(-3)

As bases are same, compare the powers.

2x = -3


\sf x = (-3)/(2)

User Frederic Lachasse
by
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