\begin{tabular}{l} (a) Simplify $$ \frac{2}{y^{0}} $$ \ (b) Simplify fully $$ \left(16 a^{4} ight)^{\frac{3}{4}} $$ \ 5 \ Factorise fully $$ 18 c^{3} d^{2}-21 c^{2} $$ \ (Total for Question 4 is 3 marks) \ \hline\end{tabular}

Question

\begin{tabular}{l} (a) Simplify $$ \frac{2}{y^{0}} $$ \ (b) Simplify fully $$ \left(16 a^{4}ight)^{\frac{3}{4}} $$ \ 5 \ Factorise fully $$ 18 c^{3} d^{2}-21 c^{2} $$ \ (Total for Question 4 is 3 marks) \ \hline\end{tabular}

UpStudy AI · Accepted Answer

Sure, let's solve each part step by step.

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### (a) Simplify $$ \frac{2}{y^{0}} $$

Any non-zero number raised to the power of 0 is 1. Therefore:

$$
\frac{2}{y^{0}} = \frac{2}{1} = 2
$$

**Answer:** $$ 2 $$

---

### (b) Simplify fully $$ \left(16 a^{4}\right)^{\frac{3}{4}} $$

Apply the exponentiation rule $$(x^{m})^{n} = x^{m \times n}$$:

$$
\left(16 a^{4}\right)^{\frac{3}{4}} = 16^{\frac{3}{4}} \times \left(a^{4}\right)^{\frac{3}{4}} 
$$

Simplify each part separately:

1. **Simplify $$16^{\frac{3}{4}}$$:**
   $$
   16 = 2^{4} \Rightarrow 16^{\frac{3}{4}} = \left(2^{4}\right)^{\frac{3}{4}} = 2^{3} = 8
   $$

2. **Simplify $$\left(a^{4}\right)^{\frac{3}{4}}$$:**
   $$
   \left(a^{4}\right)^{\frac{3}{4}} = a^{3}
   $$

Combine both results:

$$
\left(16 a^{4}\right)^{\frac{3}{4}} = 8a^{3}
$$

**Answer:** $$ 8a^{3} $$

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### (5) Factorise fully $$ 18 c^{3} d^{2} - 21 c^{2} $$

1. **Find the greatest common factor (GCF):**
   - Coefficients: GCF of 18 and 21 is 3.
   - Variables: Both terms have $$c^{2}$$.

2. **Factor out the GCF:**
   $$
   18 c^{3} d^{2} - 21 c^{2} = 3c^{2} \left(6c d^{2} - 7\right)
   $$

**Answer:** $$ 3c^{2} (6c d^{2} - 7) $$

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**Summary of Answers:**

- **(a)** $$ 2 $$
- **(b)** $$ 8a^{3} $$
- **Factorised Form:** $$ 3c^{2} (6c d^{2} - 7) $$
- **(a)** $$ 2 $$ - **(b)** $$ 8a^{3} $$ - **Factorised Form:** $$ 3c^{2} (6c d^{2} - 7) $$

(a) Simplify

(b) Simplify fully

5

Factorise fully

(Total for Question 4 is 3 marks)

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Solución

(a) Simplify

(b) Simplify fully

(5) Factorise fully

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(a) Simplify (b) Simplify fully 5 Factorise fully (Total for Question 4 is 3 marks)