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Work out the value of $$\frac{3^y \times 3^{y-2}}{3^3}$$ - Edexcel - GCSE Maths - Question 2 - 2018 - Paper 1

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Work out the value of $$\frac{3^y \times 3^{y-2}}{3^3}$$

Worked Solution & Example Answer:Work out the value of $$\frac{3^y \times 3^{y-2}}{3^3}$$ - Edexcel - GCSE Maths - Question 2 - 2018 - Paper 1

Step 1

First Step: Simplifying the Expression

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Answer

To simplify the expression, we can use the laws of indices. First, we combine the powers in the numerator:

3y×3y−2=3y+(y−2)=32y−23^y \times 3^{y-2} = 3^{y + (y - 2)} = 3^{2y - 2}

Now substituting back into the expression, we have:

32y−233\frac{3^{2y - 2}}{3^3}

Step 2

Final Step: Applying the Quotient Rule

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Answer

Using the quotient rule of indices, which states that:

aman=am−n\frac{a^m}{a^n} = a^{m-n}

we can simplify the expression as:

3(2y−2)−3=32y−53^{(2y - 2) - 3} = 3^{2y - 5}

Thus, the final simplified expression is:

32y−53^{2y - 5}

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