Question

Find the value of$a{b}^n$iflocalid="1646746061753" $n=3,a=2000,$$b=-\frac{1}{5}$

Short answer

Value of$a{b}^n$ is$-16$

Step-by-step solution

- Substitute given values

Substitute 2000 for $a$, $-\frac{1}{5}$for $b$, and 3 for$n$

$a{b}^n=2000{\left(-\frac{1}{5}\right)}^3$

- Order of simplification

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

- Simplify 2000-153

To evaluate the value of the given expression, first expand the exponentthen perform multiplication as shown below

$\begin{array}{c}2000{\left(-\frac{1}{5}\right)}^3=2000\left(-\frac{1}{125}\right)\\ =-\frac{2000}{125}\\ =-16\end{array}$

Thus, value of $a{b}^n$is$-16$