Question

Simplify (8.1)(8.12)4. (8.1)6 (8.1)7 (8.1)8 (8.1)9

Answer 1

To simplify the expression, use the properties of exponents by adding the exponents for numbers with the same base and then combine like terms.

Step-by-step explanation:

To simplify the expression (8.1)(8.12)4. (8.1)6 (8.1)7 (8.1)8 (8.1)9, we can use the properties of exponents. When multiplying numbers with the same base, you add the exponents. So, (8.1)(8.12)4 can be written as 8.14. Next, to simplify (8.1)6 (8.1)7 (8.1)8 (8.1)9, we can again add the exponents: 8.16 + 8.17 + 8.18 + 8.19.

Combining like terms, we get 8.14 + 8.16 + 8.17 + 8.18 + 8.19, which can be further simplified by adding the numbers together to get the final answer.

Answer 2

To simplify the expression (8.1)(8.12)^4, multiply the numbers together and apply the exponent. The simplified expression is approximately 34822.674. To check the answer, divide the expression by 8.1 and compare it to 8.12^4. The values are approximately equal.

Step-by-step explanation:

Simplifying the expression:

(8.1)(8.12)^4

To simplify, multiply the numbers together:

(8.1)(8.12)^4 = (8.1)(8.12)(8.12)(8.12)(8.12)

Then apply the exponent to each factor:

(8.1)(8.12)^4 = (8.1)(8.12)^3(8.12)

Finally, calculate the value of (8.12)^3:

(8.12)^3 = 8.12 x 8.12 x 8.12 = 538.95

Now substitute the value back into the expression:

(8.1)(538.95)(8.12) = 34822.674

Checking the answer:

Divide the expression by 8.1 and check if the result is approximately equal to 8.12^4:

34822.674 / 8.1 = 4305.07407

8.12^4 = 538.95^4 = 4348.52214

Since the two values are approximately equal, the answer is reasonable.