Q 1.37. Simplify:(a) -34(b)聽-34... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 1: Q 1.37. (page 33)

Simplify:
(a) ${(- 3)}^{4}$
(b) $- 3^{4}$

Short Answer

Expert verified

(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, $a^{n} = \underset{n f a c t o r s}{\underset{铃�}{a 路 a 路鈰� 路 a}}$ .

Part (a). Step 2. Expanded Form.

Write the given exponent in expanded form using the definition of exponential form, $a^{n} = \underset{n f a c t o r s}{\underset{铃�}{a 路 a 路鈰� 路 a}}$ .

${(- 3)}^{4} = (- 3) (- 3) (- 3) (- 3)$

Part (a). Step 3. Multiply.

Perform multiplication to simplify the obtained expression.

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

Part (a). Step 4. Conclusion.

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

Part (b). Step 1. Concept Used.

The exponential notation $a^{n}$ represents the product of $n$ factors of $a$ , that is, $a^{n} = \underset{n f a c t o r s}{\underset{铃�}{a 路 a 路鈰� 路 a}}$ .

Part (b). Step 2. Expanded Form.

Write the given exponent using the definition of exponential form, $a^{n} = \underset{n f a c t o r s}{\underset{铃�}{a 路 a 路鈰� 路 a}}$ .

$- 3^{4} = - (3 路 3 路 3 路 3)$

Part (b). Step 3. Multiply.

Perform multiplication to simplify the obtained expression.

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

Part (b). Step 4. Conclusion.

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

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91影视

Simplify:
(a) ${(- 3)}^{4}$
(b) $- 3^{4}$

Short Answer

Step by step solution

Part (a). Step 1. Concept Used.

Part (a). Step 2. Expanded Form.

Part (a). Step 3. Multiply.

Part (a). Step 4. Conclusion.

Part (b). Step 1. Concept Used.

Part (b). Step 2. Expanded Form.

Part (b). Step 3. Multiply.

Part (b). Step 4. Conclusion.

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91影视

Simplify:(a) -34(b)-34

Short Answer

Step by step solution

Part (a). Step 1. Concept Used.

Part (a). Step 2. Expanded Form.

Part (a). Step 3. Multiply.

Part (a). Step 4. Conclusion.

Part (b). Step 1. Concept Used.

Part (b). Step 2. Expanded Form.

Part (b). Step 3. Multiply.

Part (b). Step 4. Conclusion.

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Study anywhere. Anytime. Across all devices.

Simplify:
(a) ${(- 3)}^{4}$
(b) $- 3^{4}$