Find the numerical equivalent of 2^5 ⋅ 2^−2

Question

options:

128
128

16
16

2
2

8

Answer 1

To find the numerical equivalent of \( 2^5 \cdot 2^{-2} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

Applying this to our expression:

\[ 2^5 \cdot 2^{-2} = 2^{5 + (-2)} = 2^{5 - 2} = 2^3 \]

Now, calculate \( 2^3 \):

\[ 2^3 = 8 \]

Thus, the numerical equivalent of \( 2^5 \cdot 2^{-2} \) is \( 8 \).

The correct option from the given choices is:

8