“Both are powers of the same variable,” what exactly does this mean? Can someone please explain.
x^8 is an example of a power, the base is x and the exponent is 8
x^2 and x^3 would be powers of the same variable
a^5 and x^4 would not
Since a and x aren’t the same????
The phrase "Both are powers of the same variable" means that two mathematical expressions involve raising the same variable to a certain exponent or power.
To understand this, let's consider an example. Suppose we have two expressions: x^2 and x^3. In both cases, the variable involved is "x," and it is being raised to a certain power (exponent). Here, x^2 means x raised to the power of 2 (x squared), and x^3 means x raised to the power of 3 (x cubed).
By stating that "Both are powers of the same variable," we are emphasizing that "x" is the common variable in both expressions. It indicates that we are working with expressions involving the same letter or symbol, but being raised to different powers.
In general, when we have expressions with the same variable raised to different powers, we can compare and analyze them to understand their relationship or solve equations involving these expressions.