https://file.aiquickdraw.com/mathbot/file/1739921396401qfluwtj2.jpg

The expression in the image appears to be \( 27^{-\frac{4}{3}} \).

This is a power with a negative exponent and a fractional exponent. Let's break it down:

1. The negative exponent means that we should take the reciprocal of the base and then apply the positive exponent.
2. The fractional exponent \( \frac{4}{3} \) means we should first take the cube root of the base and then raise the result to the 4th power.

To simplify \( 27^{-\frac{4}{3}} \):

1. First, take the reciprocal because of the negative exponent:
   \[
   27^{-\frac{4}{3}} = \frac{1}{27^{\frac{4}{3}}}
   \]

2. Now, simplify \( 27^{\frac{4}{3}} \). Since 27 is \( 3^3 \), we can rewrite it as:
   \[
   27^{\frac{4}{3}} = (3^3)^{\frac{4}{3}} = 3^4 = 81
   \]

3. So, the final result is:
   \[
   27^{-\frac{4}{3}} = \frac{1}{81}
   \]

Would you like any further explanation or help with similar problems?

Here are some related questions to explore further:
1. How do you simplify exponents with different bases?
2. What is the significance of negative exponents in algebra?
3. Can you apply the same technique to other fractional exponents, like \( 16^{\frac{3}{2}} \)?
4. How does the cube root relate to exponents and powers?
5. What is the process for dealing with a negative fractional exponent?

**Tip**: When working with fractional exponents, remember the rule: \( a^{\frac{m}{n}} = \sqrt[n]{a^m} \), where \( n \) is the root and \( m \) is the power.

The expression in the image appears to be 27^{-4/3}. Simplify the expression.

Learn how to simplify the exponent expression 27^{-4/3}. This problem involves applying the laws of exponents, including handling negative and fractional exponents. Suitable for students in Grades 8-10.

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