Q51. - Algebra 2

Question

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

Step-by-Step Solution

Answer

Value of $a{b}^n$ is $-16$

Step 1 - Substitute given values

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

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

Step 2 - 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.

Step 3 - Simplify 2000 - 1 5 3

To evaluate the value of the given expression, first expand the exponent then 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 $-16$