If (2^a \times 3^b=216), what are the correct values of (a) and (b)?
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Answer and explanation
Correct answer: (a=3, b=3)
Step 1: Write (216) as (8 \times 27). Step 2: (8=2^3) and (27=3^3), so (216=2^3 \times 3^3). Hence (a=3, b=3). Step 3: For unknown exponents, split the number into familiar powers.
Frequently asked questions
What is the correct answer to this question?
(a=3, b=3)
Why is this the correct answer?
Step 1: Write (216) as (8 \times 27). Step 2: (8=2^3) and (27=3^3), so (216=2^3 \times 3^3). Hence (a=3, b=3). Step 3: For unknown exponents, split the number into familiar powers.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Prime Factorisation.
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