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Mastering Powers and Products with Exponents

Learn how to simplify and find powers of powers and products using laws of exponents. Practice real-world examples to enhance understanding.

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Mastering Powers and Products with Exponents

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  1. Lesson Menu Main Idea Key Concept: Power of a Power Example 1: Find the Power of a Power Example 2: Find the Power of a Power Key Concept: Power of a Product Example 3: Power of a Product Example 4: Power of a Product Example 5: Real-World Example

  2. Use laws of exponents to find powers of monomials. Main Idea/Vocabulary

  3. Key Concept

  4. Find the Power of a Power Simplify (52)8. (52)8 = 52•8Power of a Power = 516 Simplify. Answer: 516 Example 1

  5. Simplify (79)3. A. 73 B. 76 C. 712 D. 727 Example 1 CYP

  6. Find the Power of a Power Simplify (a3)7. (a3)7 = a3• 7Power of a Power = a21 Simplify. Answer: a21 Example 2

  7. Simplify (d5)5. A.d25 B.d5 C.d1 D.d0 Example 2 CYP

  8. Key Concept 3

  9. Power of a Product Simplify (3c4)3. (3c4)3 = 33•c4•3Power of a Product = 27c12 Simplify. Answer: 27c12 Example 3

  10. Simplify (8r7)2. A. 8r14 B. 16r14 C. 64r9 D. 64r14 Example 3 CYP

  11. Power of a Product Simplify (–4p5q)2. (–4p5q)2 = (–4)2•p5•2•q2 Power of a Product = 16p10q2 Simplify. Answer: 16p10q2 Example 4

  12. Simplify (–6s2t9)3. A. –216s6t27 B. –216s5t12 C. –18s6t27 D. –18s5t12 Example 4 CYP

  13. GEOMETRY Find the volume of a cube with side lengths of 6mn7. Express as a monomial. V = s3 Volume of a cube V = (6mn7)3Replace s with 6mn7. V = 63(m1)3(n7)3 Power of a Product V = 216m3n21 Simplify. Answer: The volume of the cube is 216m3n21 cubic units. Example 5

  14. GEOMETRY Find the area of a square with side lengths of 5q8r5. Express as a monomial. A. 10q10r7 B. 10q16r10 C. 25q10r7 D. 25q16r10 Example 5 CYP

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