Math Problem Statement
Solution
To simplify the expression , let’s follow these steps:
-
Calculate the inner expression:
-
Rewrite the expression:
Now, substitute back into the expression: -
Apply the negative exponent:
The negative exponent means we take the reciprocal: -
Evaluate the exponent :
To evaluate , we can first find the cube root and then square the result:- The cube root of is .
- Squaring it, we get:
This gives the expression in simplified form.
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Math Problem Analysis
Mathematical Concepts
Exponents
Fractions
Reciprocal
Cube Roots
Simplification
Formulas
\left(a^m\right)^n = a^{m\cdot n}
a^{-m} = \frac{1}{a^m}
\sqrt[3]{a} = a^{1/3}
Theorems
Exponentiation rules
Reciprocal rule
Fraction exponent rules
Suitable Grade Level
Grades 8-10