If a = 2 \times 10^3 and b = 3 \times 10^{-4}, what is the value of the expression \sqrt{\… — ACT

If $a = 2 \times 10^3$ and $b = 3 \times 10^{-4}$ , what is the value of the expression $\sqrt{\frac{a^3 \cdot b^2}{1.8}}$ ?

Answer: 20

Evaluating the components of the expression sequentially:

a^3 = 8 \times 10^9

and

b^2 = 9 \times 10^{-8}

. Multiplying them yields

(8 \times 9) \times 10^{9-8} = 72 \times 10^1 = 720

. Dividing by the decimal

1.8

results in

720 / 1.8 = 400

. The square root of

400

yields

20

Calculate the value of

a^3

8 \times 10^9

Apply the power of a product rule,

(xy)^n = x^n y^n

, and the power of a power rule,

(10^p)^q = 10^{p \cdot q}

Calculate the value of

b^2

9 \times 10^{-8}

Apply the power of a product rule and power of a power rule to

(3 \times 10^{-4})^2

Multiply

a^3

and

b^2

720

Multiply the coefficients (

8 \times 9 = 72

) and add the exponents of the base 10 (

10^9 \times 10^{-8} = 10^1

), resulting in

72 \times 10 = 720

Divide the product by

1.8

400

Substitute the values to get

720 / 1.8

, which simplifies to

7200 / 18 = 400

Take the square root of the quotient

20

Find the non-negative square root of

400

, which is

20

Simplifying numerical expressions containing combinations of exponent rules, roots, and scientific notation.

Estimated Time:1m 30s

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