Simplify: 5² × 2² × 5² × 2

Correct Answer is : 23×54\;\;2³ × 5^423×54

Correct Answer is : 23×54\;\;2³ × 5^423×54

Test Index

BECE Mathematics 2016 Paper

Question : 15

Total: 40

Simplify:

5^2 \times 2^2 \times 5^2 \times 2

Solution:

Concept:

When multiplying powers with the same base, add the exponents.

Explanation:

Express every factor in exponential form.

Recall that

2 = 2^1

So,

5^2 \times 2^2 \times 5^2 \times 2 = 5^2 \times 2^2 \times 5^2 \times 2^1

Group the same bases:

(5^2 \times 5^2) \times (2^2 \times 2^1)

For base

5

, add exponents:

2 + 2 = 4

, giving

5^4

For base

2

, add exponents:

2 + 1 = 3

, giving

2^3

Therefore, the simplified expression is

2^3 \times 5^4

Answer:

2^3 \times 5^4

Hence, the correct option is D.

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