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9 (a) Write down the value of $7^0$ - Edexcel - GCSE Maths - Question 10 - 2021 - Paper 1

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9 (a) Write down the value of $7^0$. (b) Find the value of $3 imes 3^3 imes 3^{-6}$. (c) Find the value of $2^4$. d) Find the value of $27^{ rac{1}{3}}$.

Worked Solution & Example Answer:9 (a) Write down the value of $7^0$ - Edexcel - GCSE Maths - Question 10 - 2021 - Paper 1

Step 1

Write down the value of $7^0$

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Answer

According to the properties of exponents, any non-zero number raised to the power of zero equals one. Therefore, the value of 707^0 is:

70=17^0 = 1

Step 2

Find the value of $3 \times 3^3 \times 3^{-6}$

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Answer

We can simplify this expression by combining the exponents of the same base:

3×33×3−6=31+3−6=3−23 \times 3^3 \times 3^{-6} = 3^{1 + 3 - 6} = 3^{-2}

Now, converting it to fractional form gives us:

3−2=132=193^{-2} = \frac{1}{3^2} = \frac{1}{9}

Step 3

Find the value of $2^4$

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Answer

To calculate 242^4, we perform the multiplication:

24=2×2×2×2=162^4 = 2 \times 2 \times 2 \times 2 = 16

Step 4

Find the value of $27^{\frac{1}{3}}$

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Answer

The expression 271327^{\frac{1}{3}} represents the cube root of 27. Since 33=273^3 = 27, we can conclude that:

2713=327^{\frac{1}{3}} = 3

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