Q5. - Algebra 1

Question

Choose a term from the Key Vocabulary list above that best describes the given expression.

${\left(a^7\right)}^3=a^{21}$

Step-by-Step Solution

Answer

The given expression can be best described as a power of a power.

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

Step 2. Define power of a power rule.

The power of a power rule states that if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same.

${\left(x^m\right)}^n=x^{mn}$

Where, $x$ is any non-zero real number. 

Step 3. Write the best description for the expression a 7 3 = a 21 .

Observe the expression, ${\left(a^7\right)}^3=a^{21}$.

$\begin{array}{c}{\left(a^7\right)}^3=a^{7\times 3}\\ =a^{21}\end{array}$

The expression, ${\left(a^7\right)}^3=a^{21}$ involves power of a power.

So, it can be termed as a power of a power.

 

Therefore the given expression can be best described as a power of a power.