Q47 MET115 Rule of Exponents

TL;DR

Simplify the expression -2x^2y^3 * (-3xy)^2 by distributing the exponent and multiplying the terms accordingly.

Transcript

for number 47 we are going to simplify this expression -2 x^2 y 3 power * the parentheses -3x y to the second power instead of this parentheses raised to the second power to do this we have to take care of this exponent first the parentheses to the second power inide of this parenthesis everything is multiplying we have -3 x and y s in this case we... Read More

Key Insights

• 😑 Distributing the exponent is an essential step in simplifying exponential expressions.
• ❎ When multiplying negative numbers, the result becomes positive due to squaring or multiplying an even number of negatives.
• ⚾ Rules for multiplying exponents involve adding the exponents for variables with the same base.
• 😑 Paying attention to the signs of the numbers is crucial to avoid errors in simplifying expressions.

Questions & Answers

Q: How do we simplify the expression -2x^2y^3 * (-3xy)^2?

To simplify the expression, we distribute the exponent and multiply each term. This involves multiplying the coefficients, combining like terms, and applying the rules for multiplying exponents.

Q: What is the result of -3^2?

-3^2 is equal to 9. When squaring a negative number, the result becomes positive.

Q: How do we multiply the exponents for variables with the same base?

When multiplying variables with the same base, we add the exponents. For example, x^2 * x^2 = x^(2+2) = x^4.

Q: Why is it important to consider the signs of the numbers while simplifying?

It is crucial to pay attention to the signs of the numbers involved because multiplying a positive and a negative number results in a negative value. Neglecting the signs may lead to an incorrect simplified expression.

Summary & Key Takeaways

• The video discusses how to simplify the expression -2x^2y^3 * (-3xy)^2.

• By distributing the exponent and multiplying the terms, we end up with -8x^4y^7 as the simplified expression.

• It is important to remember the rules for multiplying exponents and the signs of the numbers involved.