Q23. - Algebra 1

Question

Simplify the given expression. Assume that no denominator equals zero.

$a^{-3}{b}^0{c}^6$

Step-by-Step Solution

Answer

The final expression is $\frac{c^6}{a^3}$.

Step 1. Define an expression.

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

Step 2. Define the meaning of zero exponent.

Zero exponent means for any non-zero real number raised to the power of 0 is equal to 1.

Step 3. Define negative exponent rule.

According to the negative exponent rule a number raised to a negative power is equal to one over the number raised to the positive power.

$a^{-n}=\frac{1}{a^n}$

 

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

Step 4. Simplify the expression a − 3 b 0 c 6 .

Use the property of zero exponent.

$$\begin{gathered} a^{-3}{b}^0{c}^6=\left(a^{-3}\right)\left(b^0\right)\left(c^6\right) \\ =\left(a^{-3}\right)\left(1\right)\left(c^6\right) \\ =\left(a^{-3}\right)\left(c^6\right) \end{gathered}$$

Assume that the denominator is not equal to zero.

 

Use the property of negative exponent rule.

$$\begin{gathered} \left(a^{-3}\right)\left(c^6\right)=\left(\frac{1}{a^3}\right)\left(c^6\right) \\ =\frac{c^6}{a^3} \end{gathered}$$

This is the final simplified expression.

 

Therefore the final expression is $\frac{c^6}{a^3}$.