Rule of Exponent Ex#5

TL;DR

Simplify the expression by distributing the exponents and performing the necessary calculations.

Transcript

okay let's see how to simplify this expression we have the first part is parentheses inside we have four X Plus third power y to the negative two and then all raised to the second power and this is I say multiply because there's nothing in between and you have the parenthesis we have multiplying with this part this is parenthesis 2 X 3 negative one... Read More

Key Insights

• 😑 Parentheses within an expression should be simplified separately before multiplying or combining the terms.
• ✖️ Distributing the exponents within parentheses involves multiplying the exponents with the exponents outside the parentheses.
• 🍉 Like terms can be combined by adding the exponents.
• 🐕‍🦺 Negative exponents can be converted to positive exponents by moving them to the denominator or vice versa.
• ✖️ Multiplying fractions involves multiplying the numerators and denominators separately.
• ⚾ Adding exponents is done when multiplying the same base with different exponents.

Questions & Answers

Q: How do you simplify the expression that involves parentheses and exponents?

To simplify the expression, distribute the exponents within each part of the expression and perform the necessary calculations within the parentheses separately.

Q: What are the simplified expressions of the individual parts?

The first part simplifies to 4^2 * x^6 * y^-4, and the second part simplifies to 2^-3 * x^3 * y^15.

Q: How do you multiply the simplified expressions together?

Multiply the numbers outside the parentheses, combine the like terms (add exponents) for x, and do the same for y to get the final simplified expression.

Q: What is the final answer to the expression?

The final answer is 2 * x^9 * y^11.

Summary & Key Takeaways

• The given expression involves two parts within parentheses that need to be simplified separately before multiplication.

• Distributing the exponents within each part and performing the calculations results in two simplified expressions.

• Multiplying the simplified expressions together gives the final answer.