6th Grade Math: Apply and Extend to Algebraic Expressions 30 Worksheets! - Free Printable

Problem Analysis:

The task involves evaluating several exponential expressions. The goal is to simplify each expression step by step and arrive at the correct numerical result. Let's solve each part systematically.

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Expression 1: \( 5 \times 2^4 \)

1. Evaluate the exponent:
\( 2^4 = 2 \times 2 \times 2 \times 2 = 16 \).

2. Multiply by 5:
\( 5 \times 16 = 80 \).

Result: \( 80 \)

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Expression 2: \( 12 - 3^2 \)

1. Evaluate the exponent:
\( 3^2 = 3 \times 3 = 9 \).

2. Subtract from 12:
\( 12 - 9 = 3 \).

Result: \( 3 \)

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Expression 3: \( 3^3 - 3^2 \)

1. Evaluate each exponent separately:
- \( 3^3 = 3 \times 3 \times 3 = 27 \).
- \( 3^2 = 3 \times 3 = 9 \).

2. Subtract the results:
\( 27 - 9 = 18 \).

Result: \( 18 \)

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Expression 4: \( 2^3 + 2^2 - 2^1 \)

1. Evaluate each exponent separately:
- \( 2^3 = 2 \times 2 \times 2 = 8 \).
- \( 2^2 = 2 \times 2 = 4 \).
- \( 2^1 = 2 \).

2. Perform the operations in order:
- Add \( 2^3 \) and \( 2^2 \): \( 8 + 4 = 12 \).
- Subtract \( 2^1 \): \( 12 - 2 = 10 \).

Result: \( 10 \)

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Expression 5: \( 9^2 - 11 \)

1. Evaluate the exponent:
\( 9^2 = 9 \times 9 = 81 \).

2. Subtract 11:
\( 81 - 11 = 70 \).

Result: \( 70 \)

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Expression 6: \( 12 \times 4^2 - 5^1 \)

1. Evaluate each exponent separately:
- \( 4^2 = 4 \times 4 = 16 \).
- \( 5^1 = 5 \).

2. Multiply and subtract:
- Multiply \( 12 \) by \( 4^2 \): \( 12 \times 16 = 192 \).
- Subtract \( 5^1 \): \( 192 - 5 = 187 \).

Result: \( 187 \)

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Final Answers:

1. \( 5 \times 2^4 = 80 \)
2. \( 12 - 3^2 = 3 \)
3. \( 3^3 - 3^2 = 18 \)
4. \( 2^3 + 2^2 - 2^1 = 10 \)
5. \( 9^2 - 11 = 70 \)
6. \( 12 \times 4^2 - 5^1 = 187 \)

Boxed Final Answer:

\[
\boxed{80, 3, 18, 10, 70, 187}
\]