Find the value of the expression: [tex]$27 a^0 c^3 \text { for } a=\frac{2}{3}, c=-\frac{1}{3}$[/tex]
Answer (2)
Substitute the given values into the expression.
Simplify the expression using the rule a 0 = 1 .
Calculate the value of c 3 .
Multiply the constants together to get the final value: − 1 .
Explanation
Understanding the problem We are asked to find the value of the expression 27 a 0 c 3 when a = 3 2 and c = − 3 1 .
Simplifying the expression First, recall that any non-zero number raised to the power of 0 is 1. Therefore, a 0 = 1 .
Substituting the values Now, substitute the given values of a and c into the expression: 27 a 0 c 3 = 27 ⋅ 1 ⋅ ( − 3 1 ) 3
Calculating the cube Next, calculate the value of ( − 3 1 ) 3 : ( − 3 1 ) 3 = ( − 3 1 ) × ( − 3 1 ) × ( − 3 1 ) = − 27 1
Multiplying the constants Finally, multiply the constants together: 27 × 1 × ( − 27 1 ) = 27 × ( − 27 1 ) = − 1
Examples
Understanding how to evaluate expressions with exponents and fractions is crucial in many real-world scenarios. For instance, when calculating the decay of radioactive substances, you often encounter exponential terms. Similarly, in financial calculations involving compound interest, you deal with expressions containing exponents and fractions. This exercise reinforces the fundamental skills needed to tackle these more complex problems.
After evaluating the expression 27 a 0 c 3 with the given values, we find that the answer is − 1 . This result comes from recognizing that a 0 = 1 and calculating c 3 . Therefore, the multiplication of the constants yields − 1 .
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