Question

Rewrite the given expression in the form 3^u where u is a constant or an algebraic expression.

(5√3)^x

Rewrite the expression in the form 2^u where u is an algebraic expression

(1/2)^x-3

Rewrite the expression in the form 2 Superscript u where u is an algebraic expression

9/3√3

Rewrite the expression in the form 2 Superscript u where u is an algebraic expression

16/3√2^x

Answer 1

Solution: (1) The expression
`(5√(3) )^x`
`\text{ is written as }`
`5^x3^{(x)/(2)`.

`(5√(3) )^x=5^x(√(3) )^x\\(5√(3) )^x=5^x(3^(1)/(2) )^x\\(5√(3) )^x=5^x3^(x)/(2)`

The value of u is
`(x)/(2)`.

(2) The expression
`((1)/(2))^x-3` is written as
`2^(-x)-3`.

`((1)/(2))^x-3=(2^(-1))^x-3\\((1)/(2))^x-3=2^(-x)-3`

The value of u is -x.

(3) The expression
`(9)/(3√(3) )` is written as
`√(3) (2^0)`.

`(9)/(3√(3) )=(9)/(3√(3) )((√(3))/(√(3)) )\\(9)/(3√(3) )=(9(√(3)) )/(3(3) )\\(9)/(3√(3) )=√(3) \\(9)/(3√(3) )=√(3)(2^0)`

THe value of u is 0.

(4)The expression
`\frac{16}{3(\sqrt{2^(x)} )}` is written as
`(1)/(3)(2^{4-(x)/(2)})`.

`\frac{16}{3(\sqrt{2^(x)} )}=(2^4)/(3(2^x)^(1/2))\\\frac{16}{3(\sqrt{2^(x)} )}=(1)/(3)(2^{4-(x)/(2)})`

The value of u is
`4-(x)/(2)`.