Question

Evaluate each expression if $a=12,b=0.5,c=-3$and $d=\frac{1}{3}$

$a\left[b^2\left(b+a\right)\right]$

Short answer

Expression $a\left[b^2\left(b+a\right)\right]$ results into $37.5$.

Step-by-step solution

- Order for 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.

– Substitute the value of b and c in expression

To evaluate given expression, first substitute the values 12 for a and 0.5 for b in expression.

$a\left[b^2\left(b+a\right)\right]=12\left[{\left(0.5\right)}^2\left(0.5+12\right)\right]$

– Simplification

To simplify further, solve the exponent term followed by parentheses and bracket then multiply the terms from left to right.

$\begin{array}{c}12\left[{\left(0.5\right)}^2\left(0.5+12\right)\right]=12\left[0.25\left(0.5+12\right)\right]\\ =12\left[0.25\left(12.5\right)\right]\\ =37.5\end{array}$