Simplifying expressions with exponents 2 | Algebra I | Khan Academy

TL;DR

Simplify the expression (m^3)^2 / (mx^3)^4, express the answer in exponential form, and make sure m and x are not equal to zero.

Transcript

We're asked to simplify m to the third and then that squared all over mx to the third all of that to the fourth power. And they want us to express our answer in exponential form. And then they tell us that m does not equal zero and x does not equal zero. Because if they did, then this denominator would be equal to zero if either of them did and the... Read More

Key Insights

• ⚾ Multiplying exponents with the same base involves adding the exponents.
• ⚾ When dividing variables with the same base, you subtract the exponents.
• 😑 The expression (m^3)^2 simplifies to m^6, and (mx^3)^4 simplifies to m^4x^12.

Questions & Answers

Q: How do you simplify (m^3)^2?

To simplify (m^3)^2, you multiply the exponents, so it becomes m^6.

Q: How do you simplify (mx^3)^4?

To simplify (mx^3)^4, you raise each term to the fourth power, giving you m^4x^12.

Q: Why can the fraction m^6/m^4x^12 be written as m^2/x^-12?

When dividing variables with the same base, you subtract the exponents. Hence, m^6/m^4 simplifies to m^2. Similarly, dividing x^12/x^0 (which is 1) gives you x^-12.

Q: Can the final answer be written as m^2 times x^-12?

Yes, m^2 times x^-12 is an equivalent way of expressing the simplified expression.

Summary & Key Takeaways

• The expression (m^3)^2 simplifies to m^6.

• The expression (mx^3)^4 simplifies to m^4x^12.

• The final simplified expression is m^2/x^12 or m^2 * x^-12.