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Activity Discussion Math Exponents

• # Exponents

Posted by on June 22, 2023 at 3:24 pm

Simplify: (3² × 2⁴) ÷ (6⁴ × 3⁰).

replied 12 months ago 4 Members · 3 Replies
• 3 Replies
• ### Omprakash

Member
June 22, 2023 at 3:30 pm
1

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…

• ### Rishi Raj

Member
June 22, 2023 at 3:37 pm
1

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!

• ### Prathyush

Member
June 22, 2023 at 3:28 pm
0

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).