Question

In the following exercise, simplify each expression.

(a) ${\left(-2\right)}^6$

(b)localid="1645766489878" $-2^6$

Short answer

Part (a) The simplified value is 64.

Part (b) The simplified value is -64.

Step-by-step solution

Part (a) Step 1. Concept Used.

The result of the multiplication or division of two numbers with the same sign is positive and with different signs, is negative.

Part (a) Step 2. Calculation.

Perform the following operation to simplify the given expression.

• Write the expanded form.
• Simplify by multiplication.

$\begin{array}{rcl}{\left(-2\right)}^6& =& \left(-2\right)\left(-2\right)\left(-2\right)\left(-2\right)\left(-2\right)\left(-2\right)\\ & =& 4\left(-2\right)\left(-2\right)\left(-2\right)\left(-2\right)\\ & =& -8\left(-2\right)\left(-2\right)\left(-2\right)\\ & =& 16\left(-2\right)\left(-2\right)\\ & =& -32\left(-2\right)\\ & =& 64\end{array}$

Part (b) Step 1. Concept Used.

The result of the multiplication or division of two numbers with the same sign is positive and with different signs, is negative.

Part (b) Step 2. Calculation.

Perform the following operation to simplify the given expression.

• Write the expanded form.
• Simplify by multiplication.

$\begin{array}{rcl}-2^6& =& -2\times 2\times 2\times 2\times 2\times 2\\ & =& -4\times 2\times 2\times 2\times 2\\ & =& -8\times 2\times 2\times 2\\ & =& -16\times 2\times 2\\ & =& -32\times 2\\ & =& -64\end{array}$