Question

Rewrite the function f of x equals 7 times one half to the 3 times x power using the properties of exponents.

f of x equals 7 times three sixths to the x power
f of x equals 7 times one eighth to the x power
f of x equals 21 times three sixths to the x power
f of x equals 343 times one eighth to the x power

Answer 1

f of x equals 7 times one eighth to the x power

Explanation:

Given phrase,

function f of x equals 7 times one half to the 3 times x power,

`\implies f(x) = 7((1)/(2))^(3x)`

By the power to power property of exponent,

That is,

`(a^m)^n=a^(m.n)`

`f(x) = 7(((1)/(2))^3)^x`

`f(x) = 7((1)/(8))^x`

= f of x equals 7 times one eighth to the x power