Question

Simplify:

(a) ${\left(-3\right)}^4$

(b)$-3^4$

Short answer

(a) 81

(b)$-81$

Step-by-step solution

Part (a). Step 1. Concept Used.

The exponential notation $a^n$represents the product of $n$factors of $a$, that is,$a^n=\underset{nfactors}{\underbrace{a·a·\cdots ·a}}$.

Part (a). Step 2. Expanded Form.

Write the given exponent in expanded form using the definition of exponential form, $a^n=\underset{nfactors}{\underbrace{a·a·\cdots ·a}}$.

${\left(-3\right)}^4=\left(-3\right)\left(-3\right)\left(-3\right)\left(-3\right)$

Part (a). Step 3. Multiply.

Perform multiplication to simplify the obtained expression.

$\begin{array}{rcl}\left(-3\right)\left(-3\right)\left(-3\right)\left(-3\right)& =& 9\left(-3\right)\left(-3\right)\\ & =& -27\left(-3\right)\\ & =& 81\end{array}$

Part (a). Step 4. Conclusion.

The value of the given expression is ${\left(-3\right)}^4=81$.

Part (b). Step 1. Concept Used.

The exponential notation $a^n$represents the product of $n$factors of $a$, that is, $a^n=\underset{nfactors}{\underbrace{a·a·\cdots ·a}}$.

Part (b). Step 2. Expanded Form.

Write the given exponent using the definition of exponential form, $a^n=\underset{nfactors}{\underbrace{a·a·\cdots ·a}}$.

$-3^4=-\left(3·3·3·3\right)$

Part (b). Step 3. Multiply.

Perform multiplication to simplify the obtained expression.

$\begin{array}{rcl}-\left(3·3·3·3\right)& =& -\left(9·3·3\right)\\ & =& -\left(27·3\right)\\ & =& -81\end{array}$

Part (b). Step 4. Conclusion.

The value obtained$-3^4=-81$.