Question

Simplify:

(a) $18(-4)÷{(-2)}^3$

(b) $-32÷4+(-2)(-7)$

Short answer

Part (a) 9

Part (b) 6

Step-by-step solution

Part (a) Step 1. Given Information. 

Consider the given expression,

$18(-4)÷{(-2)}^3$

Part (a) Step 2. Calculate the exponent.

The value of ${\left(-2\right)}^3$is $-8$. Simplify the exponent ${\left(-2\right)}^3$in the given expression.

$18\left(-4\right)÷\left(-8\right)$

Part (a) Step 3. Multiply.

According to the order of operations, the operations of multiplication and division should be performed from left to right.

So, multiply 18 by $-4$.

$-72÷\left(-8\right)$

Part (a) Step 4. Divide. 

Divide $-72$by $-8$.

$-72÷\left(-8\right)=9$

Part (a) Step 5. Conclusion.

The simplified value of$18(-4)÷{(-2)}^3$is 9.

Part (b) Step 1. Given Information.  

Consider the given expression,

$-32÷4+(-2)(-7)$

Part (b) Step 2. Divide. 

According to the order of operations, the operations of multiplication and division should be performed from left to right.

In the given expression, the division must be performed. Divide $-32$by 4.

$-8+\left(-2\right)\left(-7\right)$

Part (b) Step 3. Multiply. 

According to the order of operations, the operations of multiplication should be performed before performing addition.

So, multiply $-2$by $-7$.

$-8+14$

Part (b) Step 4. Addition. 

Add $-8$by 14.

$-8+14=6$

Part (b) Step 5. Conclusion. 

The simplified value of $-32÷4+(-2)(-7)$is 6.