Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![### Simplifying the Expression
#### Problem Statement:
Simplify the expression. Write the expression without using negative exponents, if possible.
\[ \left( \frac{64}{27} \right)^{-\frac{2}{3}} \]
#### Steps to Simplify:
1. **Understand the Negative Exponent**:
The expression \(\left( \frac{64}{27} \right)^{-\frac{2}{3}}\) contains a negative exponent. A negative exponent indicates the reciprocal of the base raised to the positive exponent:
\[ \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^n \]
2. **Apply the Rule**:
Convert the negative exponent to a positive exponent by taking the reciprocal of the base:
\[ \left( \frac{64}{27} \right)^{-\frac{2}{3}} = \left( \frac{27}{64} \right)^{\frac{2}{3}} \]
3. **Simplify the Fraction**:
Break down \( \left( \frac{27}{64} \right)^{\frac{2}{3}}\):
\[
\left( \frac{27}{64} \right)^{\frac{2}{3}} = \left( \frac{27^{\frac{1}{3}}}{64^{\frac{1}{3}}} \right)^2
\]
4. **Calculate the Cube Roots and Exponent**:
\[
27^{\frac{1}{3}} = 3 \quad \text{and} \quad 64^{\frac{1}{3}} = 4
\]
Therefore,
\[
\left( \frac{27}{64} \right)^{\frac{2}{3}} = \left( \frac{3}{4} \right)^2 = \frac{9}{16}
\]
#### Final Answer:
\[
\boxed{\frac{9}{16}}
\]
This method ensures that the expression is simplified without using negative exponents, as requested.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef7f77a8-174f-4382-a461-22b0c5210f9d%2F44ae1226-1df0-4f12-9552-6a7a45619d3a%2Fivrnnhe_processed.png&w=3840&q=75)
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