Simplify x^675/x^453

When dividing two exponential expressions with the same base, you subtract the exponents. Therefore, x^675 / x^453 simplifies to x^(675 - 453), which is x^222.

What is the missing exponent in the following equation?

e?/e^65 = e^38

The missing exponent can be found by subtracting the exponent of the denominator from the exponent of the numerator. Since the base is the same (e), the missing exponent is the difference between 65 and 38, which is:

e^(65 - 38) = e^27

that is incorrect

Apologies for the mistake. Let's correct it.

The equation e^? / e^65 = e^38 can be solved by subtracting the exponents. Since the base is the same (e), we have:

e^(? - 65) = e^38

To make the bases equal, we can set the exponents equal:

? - 65 = 38

Adding 65 to both sides:

? = 38 + 65

? = 103

Therefore, the missing exponent is 103.

Simplify 13^12÷13^−10

.(1 point)

When dividing two exponential expressions with the same base, you subtract the exponents. Therefore, 13^12 ÷ 13^(-10) simplifies to 13^(12 - (-10)), which is 13^(12 + 10).

13^(12 + 10) can be further simplified as:

13^22

Simplify 4^13÷3^−5

When dividing two exponential expressions with the same base, you subtract the exponents. Therefore, 4^13 ÷ 3^(-5) simplifies to 4^13 * 3^(5).

Now we have the product of two exponential expressions with different bases. There are no further simplifications possible, so the expression remains as:

4^13 * 3^5

simplify this expression using the Quotient Rule of Integer Exponents: t^400/t.^100.(1 point)

t^500

t^300

300

t^4

Using the Quotient Rule of Integer Exponents, we subtract the exponents of t in the numerator and denominator.

Thus, t^400 / t^100 simplifies to t^(400 - 100) = t^300.

Therefore, the simplified expression is t^300.

Simplify a^67b^34.(1 point)

Responses

23
23

a67b34
Start Fraction a superscript 67 baseline over b superscript 34 baseline End Fraction

a33
a superscript 33 baseline

ab33

The simplified expression is a^67 * b^34.

Apply the Quotient Rule of Integer Exponents to simplify 23^65÷23^32.(1 point)

Responses

2333
23 superscript 33 baseline

97
97

2397
23 superscript 97 baseline

133

Using the Quotient Rule of Integer Exponents, we subtract the exponents of 23 in the denominator from the exponents of 23 in the numerator.

23^65 ÷ 23^32 simplifies to 23^(65 - 32) = 23^33.

Therefore, the simplified expression is 23^33.

Simplify this expression using the Quotient Rule of Integer Exponents: 1253÷753.(1 point)

Responses

12^53÷7^53

5^106

12^106

5^53