34.1k views
3 votes
Use the power rule, the power ((-9x³z³)/(y⁴))³

User Kaka Ruto
by
7.7k points

1 Answer

6 votes

Final answer:

Applying the power rule, the expression ((-9x³z³)/(y⁴))³ simplifies to -729x¹z¹/y⁻¹² by cubing each part of the fraction and applying the power to each variable and coefficient.

Step-by-step explanation:

Applying the Power Rule to an Exponential Expression:

To apply the power rule to the expression ((-9x³z³)/(y⁴))³, you must raise each part of the fraction to the third power. Start by cubing the coefficient -9 to obtain -729. Next, apply the power of 3 to each variable separately, multiplying the exponents: x³ raised to the third power is x¹, and z³ raised to the third power is z¹. Since y⁴ is in the denominator, its exponent is negative; raising y⁴ to the third power gives us y⁻¹². As a result, the simplified expression is -729x¹z¹/y⁻¹².

Remember that a negative exponent indicates division. Negative exponents, such as x⁻⁴, equate to 1 divided by x´, flipping the base to the denominator; hence, y⁻¹² becomes 1/y⁻¹².

User Cathyjo
by
6.9k points

Related questions

1 answer
4 votes
190k views
asked Apr 6, 2018 47.2k views
DenEwout asked Apr 6, 2018
by DenEwout
8.4k points
2 answers
1 vote
47.2k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories