I'll solve each of these exponent problems step by step.
1. 3² • 3⁴
When multiplying with the same base, add exponents: 3^(2+4) = 3⁶
2. x⁸ • x⁵
Add exponents: x^(8+5) = x¹³
3. 3x² • 4x²
Multiply coefficients and add exponents: (3•4)x^(2+2) = 12x⁴
4. x²y⁴ • xy¹²
Add exponents for each variable: x^(2+5)y^(4+12) = x⁷y¹⁶
5. (5²)³
Power to a power - multiply exponents: 5^(2×3) = 5
6. (x⁴)
Multiply exponents: x^(4×5) = x²⁰
7. (2x)⁴
Apply exponent to both parts: 2⁴x⁴ = 16x⁴
8. (x⁴y⁵)³
Multiply each exponent by 3: x^(4×3)y^(5×3) = x¹²y¹⁵
9. (3x⁴y²z³)²
Square everything: 3²x^(4×2)y^(2×2)z^(3×2) = 9xy⁴z⁶
10. (2x²)³(-3x²y)²
First part: 2³x = 8x⁶
Second part: (-3)²x⁴y² = 9x⁴y²
Multiply together: 8x⁶ • 9xy² = 72x¹⁰y²
11. 3⁻⁴
Negative exponent means reciprocal: 1/3⁴ = 1/81
12. 8⁵/8³
Subtract exponents when dividing: 8^(5-3) = 8² = 64
13. 27⁰
Any non-zero number to the zero power equals 1
14. 12x⁵/4x²
Divide coefficients and subtract exponents: (12/4)x^(5-2) = 3x³
15. 2x⁵y⁷/16x⁴y
Simplify: (2/16)x^(5-4)y^(7-1) = (1/8)xy⁶ = xy⁶/8
16. 3⁵/3⁷
Subtract exponents: 3^(5-7) = 3⁻² = 1/3² = 1/9
17. 4x⁵y²/20x⁷y⁵
Simplify coefficients: 4/20 = 1/5
Subtract exponents: x^(5-7)y^(2-5) = x⁻²y⁻³ = 1/(5x²y³)
18. 12xy²/3x⁵y⁷
Simplify coefficients: 12/3 = 4
Subtract exponents: x^(1-5)y^(2-7) = x⁻⁴y⁻⁵ = 4/(x⁴y⁵)
19. (2x⁴/3x)
First simplify inside: 2x⁴/3x = (2/3)x³
Then apply power: (2/3)(x³)⁵ = 32/243 • x¹⁵ = 32x¹⁵/243
20. 18x⁻⁴y⁶/12x⁻²y³
Simplify coefficients: 18/12 = 3/2
Subtract exponents: x^(-4-(-2))y^(6-(-3)) = x²y⁹
Final answer: 3y⁹/(2x²)
Final Answer:
1. 3⁶
2. x¹³
3. 12x⁴
4. x⁷y¹⁶
5. 5⁶
6. x²⁰
7. 16x⁴
8. x¹²y¹
9. 9x⁸y⁴z⁶
10. 72x¹⁰y²
11. 1/81
12. 64
13. 1
14. 3x³
15. xy⁶/8
16. 1/9
17. 1/(5x²y³)
18. 4/(x⁴y⁵)
19. 32x¹⁵/243
20. 3y⁹/(2x²)
Parent Tip: Review the logic above to help your child master the concept of laws of exponents practice worksheet.
