Evaluate Powers Expressions: (4/9)^(3/2) and (-27)^(-1/3)

In summary, for the first problem, \left(\frac{4}{9}\right)^\frac{3}{2}, we can rewrite it as \left(\sqrt[2]{\frac{4}{9}}\right)^3, which simplifies to \left(\frac{2}{3}\right)^3, and the final answer is \frac{8}{27}. For the second problem, (-27)^-^\frac{1}{3}, we can rewrite it as \left(\frac{1}{(-27)}\right)^\frac{1}{3}, which simplifies to \left(-\frac{1}{27}\
  • #1
Raza
203
0
Evalulate, leaving the answer as a fraction:


a) [tex]\left(\frac{4}{9}\right)^\frac{3}{2}[/tex]


b) [tex](-27)^-^\frac{1}{3}[/tex]

Please Help.
Thanks
 
Physics news on Phys.org
  • #2
Some useful hints:

[tex] a^\frac{b}{c} = (a^b)^\frac{1}{c} = (a^\frac{1}{c})^b [/tex]

[tex] a^-^b = \frac{1}{a}^b [/tex]

[tex] a^\frac{1}{b} = \sqrt{a} [/tex]

hope that helps
 
  • #3
And to add on to Imo's hints, remember that an exponent is written in the form of [tex]\frac{\mbox{power}}{\mbox{root}}[/tex]

For instance, [tex]9^{\frac{3}{2}} = (\sqrt{9})^3[/tex]
 
  • #4
Thank you, I finally got it. I lost my math notes and my exam is coming pretty soon so I needed to review.
 
  • #5
[tex]a^-^b = \frac{1}{a^b} = \left(\frac{1}{a}\right)^b [/tex]
 

FAQ: Evaluate Powers Expressions: (4/9)^(3/2) and (-27)^(-1/3)

What is a power expression?

A power expression is a mathematical expression that involves raising a number or variable to a certain power, also known as an exponent. It is written in the form of an, where a is the base and n is the exponent.

What is the difference between a power expression and a radical expression?

A power expression involves raising a number or variable to a certain power, while a radical expression involves finding the root of a number or variable. They are inverse operations of each other, as an and √an cancel each other out.

What are some common properties of power expressions?

Some common properties of power expressions are the product rule, quotient rule, and power rule. The product rule states that when two power expressions with the same base are multiplied, the exponents can be added. The quotient rule states that when two power expressions with the same base are divided, the exponents can be subtracted. And the power rule states that when a power expression is raised to another power, the exponents can be multiplied.

How are power expressions used in real life?

Power expressions are used in various applications such as physics, engineering, and finance. In physics, power expressions are used to calculate work, energy, and power. In engineering, they are used to model relationships between different variables. And in finance, they are used to calculate compound interest and growth rates.

What are some common mistakes to avoid when working with power expressions?

Some common mistakes to avoid when working with power expressions include forgetting to apply the correct exponent rules, not simplifying expressions fully, and mixing up the order of operations. It is important to carefully follow the rules of exponents and simplify expressions as much as possible to avoid errors.

Back
Top