Arrange the following mathematical expressions in order from least to greatest value.

The correct order of the expressions from least to greatest is

2^3 \times 5^2

4 \times 10^2

\sqrt{2.5 \times 10^5}

, and

0.06 \times 10^4

Evaluating each term yields

2^3 \times 5^2 = 200

4 \times 10^2 = 400

\sqrt{2.5 \times 10^5} = 500

, and

0.06 \times 10^4 = 600

. Comparing these simplified values shows that

200 < 400 < 500 < 600

, confirming the correct sequence.

Evaluate the expression with bases 2 and 5.

2^3 \times 5^2 = 8 \times 25 = 200

First compute the exponential terms and then multiply the resulting values.

Evaluate the expression in standard scientific notation.

4 \times 10^2 = 4 \times 100 = 400

Multiply 4 by the value of

10^2

Evaluate the square root expression.

\sqrt{2.5 \times 10^5} = \sqrt{25 \times 10^4} = 5 \times 10^2 = 500

Adjust the expression under the square root to make it easier to simplify:

2.5 \times 10^5 = 25 \times 10^4

. The square root of 25 is 5, and the square root of

10^4

10^2

Evaluate the non-standard power of ten expression.

0.06 \times 10^4 = 0.06 \times 10,000 = 600

Multiply the decimal coefficient by the power of ten by shifting the decimal point four places to the right.

Compare and order all the simplified values.

200 < 400 < 500 < 600

Sort the values from least to greatest to determine the correct order.

Evaluating expressions involving powers, roots, and scientific notation to compare their values.

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