QQuestionMathematics
QuestionMathematics
"What expression is equivalent to 4^−3?
A. 1 / 4^3
B. 4^3
C. 1 / 64
D. 64"
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the meaning of a negative exponent
- The general rule is: $$a^{-n} = \frac{1}{a^{n}}
- A negative exponent means we need to take the reciprocal of the base raised to the positive exponent
Step 3:: Apply the rule to 4^{- 3}
4^{-3} = \frac{1}{4^{3}}
- Following the negative exponent rule:
Step 4:: Calculate 4^{3}
- $$4^{3} = 4 \times 4 \times 4 = 64
Step 5:: Complete the calculation
- $$4^{-3} = \frac{1}{4^{3}} = \frac{1}{64}
Step 6:: Check the given options
- $$\frac{1}{64}$$ corresponds to option C
Final Answer
Explanation: The negative exponent means we take the reciprocal of 4^{3}, which is 1 / 64.
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