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Simplify: (a) $4a^1 \times 3a^2$ (b) $ \left( \frac{2a^2}{a^3} \right)^3 $ - OCR - GCSE Maths - Question 14 - 2020 - Paper 1

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Question 14

Simplify:--(a)-$4a^1-\times-3a^2$--(b)-$-\left(-\frac{2a^2}{a^3}-\right)^3-$-OCR-GCSE Maths-Question 14-2020-Paper 1.png

Simplify: (a) $4a^1 \times 3a^2$ (b) $ \left( \frac{2a^2}{a^3} \right)^3 $

Worked Solution & Example Answer:Simplify: (a) $4a^1 \times 3a^2$ (b) $ \left( \frac{2a^2}{a^3} \right)^3 $ - OCR - GCSE Maths - Question 14 - 2020 - Paper 1

Step 1

(a) Simplify $4a^1 \times 3a^2$

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Answer

To simplify the expression, we can first multiply the coefficients and then apply the properties of exponents for the variables:

  1. Multiply the coefficients:

    • 4×3=124 \times 3 = 12

  2. Combine the variables using the property that am×an=am+na^m \times a^n = a^{m+n}:

    • a1×a2=a1+2=a3a^1 \times a^2 = a^{1+2} = a^3

Putting it all together, we have: 12a312a^3

Step 2

(b) Simplify $\left( \frac{2a^2}{a^3} \right)^3$

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Answer

To simplify this expression, follow these steps:

  1. Simplify the fraction inside the parentheses:

    • Using the property of exponents, we can reduce the expression: 2a2a3=2⋅a2−3=2⋅a−1=2a\frac{2a^2}{a^3} = 2 \cdot a^{2-3} = 2 \cdot a^{-1} = \frac{2}{a}

  2. Now raise the simplified fraction to the power of 3:

    • (2a)3=23a3=8a3\left( \frac{2}{a} \right)^3 = \frac{2^3}{a^3} = \frac{8}{a^3}

Thus, the final answer is: 8a3\frac{8}{a^3}

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