Equations » Power equations

A power formula is always of the form y = ax^b.
A power equation is always of the form ax^b = c.

One or two solutions?

A power equation always has one solution when you have an odd exponent.
A power equation has two, one or zero solutions when you have an even exponent.
Think of a quadratic equation (even exponent):
x² = 4 has two solutions, namely x = –2 or x = 2.
x² = 0 has one solution, namely x = 0.
x² = –1 has no solutions.

Root = power

Every root can be written as a power.
The rule is n-th root of x = x.

Example 1

3`x`⁴ + 8	= 1883
3`x`⁴	= 1875
`x`⁴	= 625
`x` = –	of `x` =
`x` = –5	or `x` = 5

Example 2

500 – 2`x`⁵	= 14
2`x`⁵	= 486
`x`⁵	= 243
`x`	= = 3

Example 3

7`x`³ + 6	= –204
7`x`³	= –210
`x`³	= –30
`x`	= ≈ –3.107

Example 4
On the graph of y = 112x^0.43 lies point (x; 14.5).
Calculate x. Round to 4 decimals.

Answer:

14.5 =	112`x`^0.43
`x`^0.43 =	14.5112
`x` =	14.5112 ≈ 0.0086