Asked by Kim asma


Write the following infinite decimal expansion as a fraction. You do not need to simplify.



0.53‾0.\overline{53}0.
53
Answered by Kim asma
The hypotenuse of a triangle was 3 cm and the hypotenuse of the final triangle was 6 cm. What is the scale factor?
Answered by Kim asma
Simplify 5^10 ⋅ 5 and write your answer in exponential form.
Answered by Kim asma

Simplify 7^15 . 7^-5 and write your answer in exponential form
Answered by Kim asma
Fully simplify and write your answer in exponential form with positive exponents only.
6^-3 . 6 . 6^-6
Answered by Kim asma
Simplify the following and leave your answer in exponential form.
7^17/7^-2
Answered by GPT 3.5
To write the infinite decimal expansion as a fraction, we can convert it into a geometric series.

Let x = 0.530530530...

Multiplying both sides of the equation by 1000, we get:

1000x = 530.530530...

Subtracting the original equation from the new equation, we get:

1000x - x = 530.530530... - 0.530530530...

Simplifying, we have:

999x = 530

Dividing both sides of the equation by 999, we get:

x = 530/999

Therefore, the infinite decimal expansion 0.530530530... is equal to the fraction 530/999.
Answered by GPT 3.5
The scale factor is the ratio of the lengths of corresponding sides in the two similar triangles.

Let's call the length of the original side of the triangle x, and the corresponding side in the final triangle y.

In the original triangle, we have:

x² + (3 cm)² = (hypotenuse of the original triangle)²
x² + 9 = 9
x² = 0

In the final triangle, we have:

y² + (6 cm)² = (hypotenuse of the final triangle)²
y² + 36 = 36
y² = 0

Since the length of both sides is 0, we can say that x = y = 0.

Therefore, the scale factor is 0.
Answered by GPT 3.5
To simplify and write the answer in exponential form, we can add the exponents since we are multiplying powers with the same base:

5^10 ⋅ 5 = 5^(10 + 1)

Simplifying the exponent:

5^(10 + 1) = 5^11

Therefore, the simplified form in exponential form is 5^11.
Answered by GPT 3.5
To simplify 7^15 ⋅ 7^-5 and write the answer in exponential form, we can subtract the exponents since we are dividing powers with the same base:

7^15 ⋅ 7^-5 = 7^(15 - 5)

Simplifying the exponent:

7^(15 - 5) = 7^10

Therefore, the simplified form in exponential form is 7^10.
Answered by GPT 3.5
To fully simplify the expression 6^-3 ⋅ 6 ⋅ 6^-6 and write the answer in exponential form with positive exponents only, we can combine the terms with the same base and add the exponents:

6^-3 ⋅ 6 ⋅ 6^-6

Using the rules of exponents, we can rewrite any negative exponent as the reciprocal of the base raised to the positive exponent.

6^-3 can be rewritten as 1/6^3 and 6^-6 can be rewritten as 1/6^6.

Substituting these values, we have:

(1/6^3) ⋅ 6 ⋅ (1/6^6)

Simplifying the expression:

= 6/6^3 ⋅ 1/6^6

= 6/216 ⋅ 1/46656

= 1/36 ⋅ 1/46656

To multiply the fractions, we can multiply the numerators and multiply the denominators:

= (1 ⋅ 1)/(36 ⋅ 46656)

= 1/1679616

Therefore, the fully simplified expression in exponential form with positive exponents only is 1/1679616.
Answered by GPT 3.5
To simplify the expression 7^17/7^-2, we can use the rules of exponents to divide the terms with the same base and subtract the exponents:

7^17/7^-2 = 7^(17-(-2))

Simplifying the exponent:

7^(17-(-2)) = 7^(17+2)

= 7^19

Therefore, the simplified form in exponential form is 7^19.