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(a) Simplify $n^2 \times n^5$ (b) Simplify $\frac{c^4 d^4}{c^2 d}$ (c) Solve $\frac{5x}{2} > 7$ - Edexcel - GCSE Maths - Question 1 - 2020 - Paper 3

Question 1

$(a)-Simplify-$n^2-\times-n^5$----(b)-Simplify-$\frac{c^4-d^4}{c^2-d}$----(c)-Solve-$\frac{5x}{2}->-7$----Edexcel-GCSE Maths-Question 1-2020-Paper 3.png$

(a) Simplify $n^2 \times n^5$ (b) Simplify $\frac{c^4 d^4}{c^2 d}$ (c) Solve $\frac{5x}{2} > 7$

Worked Solution & Example Answer:(a) Simplify $n^2 \times n^5$ (b) Simplify $\frac{c^4 d^4}{c^2 d}$ (c) Solve $\frac{5x}{2} > 7$ - Edexcel - GCSE Maths - Question 1 - 2020 - Paper 3

Step 1

Simplify $n^2 \times n^5$

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Answer

To simplify this expression, we use the property of exponents that states $a^m \times a^n = a^{m+n}$ . Therefore:

$n^2 \times n^5 = n^{2+5} = n^7$

Step 2

Simplify $\frac{c^4 d^4}{c^2 d}$

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Answer

For this fraction, we can simplify using the properties of exponents:

For the $c$ terms: $\frac{c^4}{c^2} = c^{4-2} = c^2$
For the $d$ terms: $\frac{d^4}{d} = d^{4-1} = d^3$

Combining these results, we get:

$\frac{c^4 d^4}{c^2 d} = c^2 d^3$

Step 3

Solve $\frac{5x}{2} > 7$

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Answer

To solve this inequality, first eliminate the fraction by multiplying both sides by 2:

$5x > 14$

Next, divide both sides by 5:

$x > \frac{14}{5}$

This can also be approximated as:

$x > 2.8$

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