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Question

2^3/2^2
(2^2) ^3
2^8×2^−3
2^2/2^3
2^−2×2^−3

Answer 1

To simplify each expression, we can use the properties of exponents. Here are the simplified forms for each expression:

1. \( \frac{2^3}{2^2} \): Use the property \( \frac{a^m}{a^n} = a^{m-n} \) \[ \frac{2^3}{2^2} = 2^{3-2} = 2^1 = 2 \]

2. \( (2^2)^3 \): Use the property \( (a^m)^n = a^{m \cdot n} \) \[ (2^2)^3 = 2^{2 \cdot 3} = 2^6 \]

3. \( 2^8 \times 2^{-3} \): Use the property \( a^m \times a^n = a^{m+n} \) \[ 2^8 \times 2^{-3} = 2^{8 + (-3)} = 2^5 \]

4. \( \frac{2^2}{2^3} \): Use the property \( \frac{a^m}{a^n} = a^{m-n} \) \[ \frac{2^2}{2^3} = 2^{2-3} = 2^{-1} = \frac{1}{2} \]

5. \( 2^{-2} \times 2^{-3} \): Use the property \( a^m \times a^n = a^{m+n} \) \[ 2^{-2} \times 2^{-3} = 2^{-2 + (-3)} = 2^{-5} \]

Thus, the simplified forms of the expressions are:

1. \( 2 \)
2. \( 2^6 \)
3. \( 2^5 \)
4. \( \frac{1}{2} \)
5. \( 2^{-5} \)