Question

notice: the exponent only applies to what comes directly before it.

5x³
means
5xx*x

(2x)³
means
(2x)(2x)(2x)

examples:

write each of the following in expanding form.

1. 5x²
2. 3x⁵
3. -4x³

1. (2x)³
2. (-4x)²
3. (-7x)⁴

Explanation:

Step1: Apply exponent rule for \(5x^{2}\)

According to the rule \(ax^{n}=a\times x\times x\times\cdots\times x\) (\(n\) times). For \(5x^{2}\), \(n = 2\), so \(5x^{2}=5\times x\times x\)

Step2: Apply exponent rule for \(3x^{5}\)

For \(3x^{5}\), \(n = 5\), so \(3x^{5}=3\times x\times x\times x\times x\times x\)

Step3: Apply exponent rule for \(-4x^{3}\)

For \(-4x^{3}\), \(n = 3\), so \(-4x^{3}=- 4\times x\times x\times x\)

Step4: Apply exponent rule for \((2x)^{3}\)

Using \((ab)^{n}=a^{n}b^{n}\), \((2x)^{3}=(2x)\times(2x)\times(2x)\)

Step5: Apply exponent rule for \((-4x)^{2}\)

Using \((ab)^{n}=a^{n}b^{n}\), \((-4x)^{2}=(-4x)\times(-4x)\)

Step6: Apply exponent rule for \((-7x)^{4}\)

Using \((ab)^{n}=a^{n}b^{n}\), \((-7x)^{4}=(-7x)\times(-7x)\times(-7x)\times(-7x)\)

Answer:

1. \(5\times x\times x\)
2. \(3\times x\times x\times x\times x\times x\)
3. \(-4\times x\times x\times x\)
4. \((2x)\times(2x)\times(2x)\)
5. \((-4x)\times(-4x)\)
6. \((-7x)\times(-7x)\times(-7x)\times(-7x)\)