(Q17.) Sample 3 GCC Math 101/120 Common Final Intermediate Algebra

TL;DR

Learn how to solve equations with fractional exponents by factoring and combining like terms.

Transcript

for number 17 while being solve this equation X to the 2/3 power plus X to the 1/3 power minus 6 x equals 0 whenever we're trying to solve an equation that the exponent is 9 foot 1 so just like this I'd like to the 2/3 power things like that the best bet is that which are try to factor the factor result and indeed we can factor this out to show you... Read More

Key Insights

• 🍉 Factoring and combining like terms is essential when solving equations with fractional exponents.
• 🍉 The coefficients and exponents are multiplied and added to break down terms with fractional exponents.
• 😵 Cross-multiplication can be used to check if the solution is correct.
• ✊ Raising both sides of the equation to the same power helps isolate the variable and solve for X.
• 🫚 Square roots require checking the answers, but cube roots do not.

Questions & Answers

Q: How do you solve equations with fractional exponents?

To solve equations with fractional exponents, factor the equation and combine like terms. Break down the terms with fractional exponents by multiplying the coefficients and adding the exponents. Substitute the factors back into the equation and solve for X.

Q: What should be done when factoring equations with fractional exponents?

When factoring equations with fractional exponents, multiply the coefficients and add the exponents. This will simplify the terms and help in combining like terms.

Q: How can you check if the solution is correct?

To check if the solution is correct, cross multiply the factors and see if they produce the original equation. If they do, then the solution is correct.

Q: Why is it important to raise both sides of the equation to the same power?

Raising both sides of the equation to the same power is important to isolate the variable. By doing this, the exponents cancel out, allowing you to solve for X.

Summary & Key Takeaways

• To solve an equation with fractional exponents, factor the equation and combine like terms.

• Break down the terms with fractional exponents by multiplying the coefficients and adding the exponents.

• Substitute the factors back into the equation and solve for X.