OUESTION 3 3.1. Simplify: 3.1.1. $$ 99 imes 1001^{0} $$ 3.1.3. $$ 2^{-2} $$ 3.1.4. $$ \left(-3 \mathrm{xy}^{2} ight)^{2} $$ 3.2. Write the following numbers in scientific notation form. 3.2.1. 0,00056 3.2.2. 523

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OUESTION 3 3.1. Simplify: 3.1.1. $$ 99 	imes 1001^{0} $$ 3.1.3. $$ 2^{-2} $$ 3.1.4. $$ \left(-3 \mathrm{xy}^{2}ight)^{2} $$ 3.2. Write the following numbers in scientific notation form. 3.2.1. 0,00056 3.2.2. 523

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**3.1. Simplify**

**3.1.1. Simplify $$ 99 \times 1001^{0} $$**

Since any nonzero number raised to the power $$0$$ is $$1$$,
$$
1001^0 = 1.
$$
Thus,
$$
99 \times 1001^0 = 99 \times 1 = 99.
$$

**3.1.3. Simplify $$ 2^{-2} $$**

A negative exponent indicates the reciprocal of the positive exponent:
$$
2^{-2} = \frac{1}{2^2} = \frac{1}{4}.
$$

**3.1.4. Simplify $$ \left(-3xy^2\right)^{2} $$**

When raising a product to a power, each factor is raised to that power:
$$
\left(-3xy^2\right)^{2} = (-3)^2 \cdot x^2 \cdot (y^2)^2.
$$
Calculate each part:
$$
(-3)^2 = 9, \quad x^2 = x^2, \quad (y^2)^2 = y^{4}.
$$
Thus, the simplified expression is:
$$
9x^2y^4.
$$

**3.2. Write the following numbers in scientific notation**

**3.2.1. Write $$0,00056$$ in scientific notation**

Interpreting $$0,00056$$ as $$0.00056$$:
$$
0.00056 = 5.6 \times 10^{-4}.
$$
To see this, note that moving the decimal point 4 places to the right converts $$0.00056$$ into $$5.6$$.

**3.2.2. Write $$523$$ in scientific notation**

Express $$523$$ as a number between $$1$$ and $$10$$ multiplied by a power of $$10$$:
$$
523 = 5.23 \times 10^{2}.
$$
**3.1. Simplify** **3.1.1. $$ 99 \times 1001^{0} = 99 $$** **3.1.3. $$ 2^{-2} = \frac{1}{4} $$** **3.1.4. $$ \left(-3xy^2\right)^{2} = 9x^2y^4 $$** **3.2. Scientific Notation** **3.2.1. $$0.00056 = 5.6 \times 10^{-4}$$** **3.2.2. $$523 = 5.23 \times 10^{2}$$**

OUESTION 3 3.1. Simplify: 3.1.1. \( 99 \times 1001^{0} \) 3.1.3. \( 2^{-2} \) 3.1.4. \( \left(-3 \mathrm{xy}^{2}\right)^{2} \) 3.2. Write the following numbers in scientific notation form. 3.2.1. 0,00056 3.2.2. 523

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