Question
b) \( m^{8} \div\left(m^{2}\right. \) e) \( \left(t^{5} \times t^{3}\right)^{4} \) h) \( \frac{y^{7}}{y^{5} \div y^{2}} \) k) \( \left(x^{9} \div x^{3}\right)^{2} \)
Ask by Hill Warner. in Greece
Feb 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
b) \( m^6 \)
e) \( t^{32} \)
h) \( y^4 \)
k) \( x^{12} \)
Solution
Let's simplify each expression step by step:
b) Simplify m⁸ ÷ m²
• When dividing powers with the same base, subtract the exponents.
• Calculation: m⁸ ÷ m² = m^(8 – 2) = m⁶
e) Simplify (t⁵ × t³)⁴
• Inside the parentheses, multiply powers with the same base by adding the exponents: t⁵ × t³ = t^(5 + 3) = t⁸.
• Now, raise t⁸ to the 4th power by multiplying the exponents: (t⁸)⁴ = t^(8×4) = t³²
h) Simplify y⁷ ÷ (y⁵ ÷ y²)
• First simplify the division inside the denominator: y⁵ ÷ y² = y^(5 – 2) = y³.
• Now, divide y⁷ by y³: y⁷ ÷ y³ = y^(7 – 3) = y⁴
k) Simplify (x⁹ ÷ x³)²
• Inside the parentheses: x⁹ ÷ x³ = x^(9 – 3) = x⁶.
• Raising x⁶ to the 2nd power: (x⁶)² = x^(6×2) = x¹²
Final answers:
b) m⁶
e) t³²
h) y⁴
k) x¹²
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
When simplifying \( m^{8} \div m^{2} \), you apply the rule of exponents that says \( a^{m} \div a^{n} = a^{m-n} \). In this case, \( m^{8-2} \) simplifies to \( m^{6} \). So, the final answer is \( m^{6} \). This teaches you how to manage exponents and ensure you’re using the right math rules! For \( \left( t^{5} \times t^{3} \right)^{4} \), start by simplifying inside the parentheses first. Using the rule \( a^{m} \times a^{n} = a^{m+n} \), you get \( t^{5+3} = t^{8} \). Then when you raise it to the power of 4, it becomes \( t^{8 \times 4} = t^{32} \). This illustrates the power of exponent rules while multiplying and raising powers!
