Question

Which variable expression represents the following phrase?

A number raised to the ninth power

$\begin{array}{l}a.9n\\ b.9^n\\ c.n^9\\ d.\frac{9}{n}\end{array}$

Short answer

The variable expression for the given phrase is $n^9$.

Step-by-step solution

Step-1 – Concept of variable expression

A variable expression or algebraic expression consists of one or more terms including variables and numbers that are connected by algebraic operations $+,-,\times ,÷$.

Step-2 – Consider the number

Let the unknown number be n.

So, we need to find the number with an exponent 9 raised over it.

Step-3 – Write Variable expression

The term power refers to exponent. So, in order to find the expression for a number raised to the ninth power, we raise the exponent of number n by 9. That is,

$\begin{array}{l}\text{Anumberraisedtotheninthpower}=n\text{raisedtothe9thpower}\\ =n^9\end{array}$.

Thus, the variable expression for the given phrase is $n^9$.

Hence, option (c) is correct.