Simplify 1 / (2^-4) without an exponent.
Understand the Problem
The question requires simplifying the expression 1 / (2^-4) without using an exponent. This involves understanding the properties of negative exponents and reciprocals.
Answer
$16$
Answer for screen readers
$16$
Steps to Solve
- Rewrite the expression using the reciprocal property
A negative exponent means taking the reciprocal. $$ \frac{1}{2^{-4}} = 2^4 $$
- Expand the expression
$2^4$ means $2$ multiplied by itself $4$ times. $$ 2^4 = 2 \cdot 2 \cdot 2 \cdot 2 $$
- Calculate the product
Multiply the numbers together. $$ 2 \cdot 2 \cdot 2 \cdot 2 = 16 $$
$16$
More Information
The expression $1 / 2^{-4}$ simplifies to $16$. This is because a negative exponent in the denominator becomes a positive exponent in the numerator.
Tips
A common mistake is misunderstanding negative exponents and how they affect the position of a term in a fraction. Remember that $x^{-n} = 1/x^n$ and $1/x^{-n} = x^n$.
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