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Exponents
Simplify: (3² × 2⁴) ÷ (6⁴ × 3⁰).
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3 Replies
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Within each set of brackets, simplify the exponents as follows:
(3 raised to the power of 2) = 32 = 9.
24 = 16 (two to the fourth power).
64 is equal to 1296 (6 multiplied by 4)
Whenever a number is raised to the power of 0, it equals one.
Reintroduce the values that have been simplified into the expression:
(9 × 16) ÷ (1296 × 1)
Multiply the number inside the brackets: 144 1296.
144 divided by 1296 equals 1/9, or 0.1111 (rounded to four decimal places).
Answer:1/9 or 0.111
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Step 1: Evaluate the numbers with exponents. 3² = 3 × 3 = 9 2⁴ = 2 × 2 × 2 × 2 = 16 6⁴ = 6 × 6 × 6 × 6 = 1,296 3⁰ = 1 (Any number raised to the power of zero is always 1.)
Step 2: Substitute the values back into the expression. (9 × 16) ÷ (1,296 × 1)
Step 3: Simplify further. 9 × 16 = 144 1,296 × 1 = 1,296
Step 4: Final answer. 144 ÷ 1,296 = 0.111111…
So, the simplified form of (3² × 2⁴) ÷ (6⁴ × 3⁰) is approximately 0.111111…
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3^0=1 (as anything raised power 0 is equal to 1) so we can just simply put 1 in place of 3^0 in denominator.
Now, we have 3^2 * 2^4 in numerator and 6^4 in denominator.
6^4 can also be written as (2*3)^4 which is equal to 2^4 * 3^4.
Now, 2^4 will got cancelled from num. and deno. and 3^4 can be written as 3^2 * 3^2 one of this 3^2 will also get cancelled and we will left only with 3^2 in the denominator.
So, the answer will be: 1/9.
Thank you!
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This reply was modified 1 year, 10 months ago by Rishi Raj Gupta.
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This reply was modified 1 year, 10 months ago by
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