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Complete the power of 2 for each statement by writing the missing value in the box - OCR - GCSE Maths - Question 12 - 2020 - Paper 3

Question 12

Complete the power of 2 for each statement by writing the missing value in the box. (i) $2^3 \times 2^3 = 2^{?}$ (ii) $\frac{1}{32} = 2^{?}$ (b) $2 \times 2^y = 1... show full transcript

Worked Solution & Example Answer:Complete the power of 2 for each statement by writing the missing value in the box - OCR - GCSE Maths - Question 12 - 2020 - Paper 3

Step 1

(i) $2^3 \times 2^3 = 2^{?}$

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Answer

To solve for the missing exponent, we can use the property of exponents which states that when multiplying like bases, we can add the exponents:

$2^3 \times 2^3 = 2^{3+3} = 2^6.$

Therefore, the missing value is 6.

Step 2

(ii) $\frac{1}{32} = 2^{?}$

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Answer

To find the exponent that makes the statement true, we express 32 as a power of 2:

$32 = 2^5.$

Thus, we can write:

$\frac{1}{32} = 2^{-5}.$

So, the missing value is -5.

Step 3

(b) $2 \times 2^y = 1$

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Answer

To isolate $y$ , we first rewrite 1 as a power of 2:

$1 = 2^0.$

So, we have:

$2 \times 2^y = 2^0.$

This can be simplified to:

$2^{1 + y} = 2^0.$

Since the bases are the same, we equate the exponents:

$1 + y = 0.$

Solving for $y$ gives:

$y = -1.$

Thus, the value of $y$ is -1.

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