What is the value of the expression 2^3 \cdot 2^2 - \sqrt{81}? — ACT

What is the value of the expression $2^3 \cdot 2^2 - \sqrt{81}$ ?

To evaluate the expression, follow the order of operations. First, simplify the exponential multiplication:

2^3 \cdot 2^2 = 2^{3+2} = 2^5 = 32

. Next, evaluate the square root:

\sqrt{81} = 9

. Finally, perform the subtraction:

32 - 9 = 23

. Thus, the correct value is 23.

Simplify the exponential term

2^3 \cdot 2^2

2^5 = 32

When multiplying exponential terms with the same base, add their exponents:

3 + 2 = 5

Evaluate the square root term

\sqrt{81}

9

The square root of 81 is the positive number that, when multiplied by itself, equals 81, which is 9.

Perform the subtraction:

32 - 9

23

Subtract 9 from 32 to find the final value of the expression.

Simplifying numerical expressions using laws of exponents, square roots, and order of operations

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