QuestionFind the missing exponent in $\frac{e^{?}}{e^{65}}=e^{38}$ .

Studdy Solution

STEP 1

Assumptions1. The base of the exponential expressions is e (uler's number, approximately equal to.71828) . The exponent in the denominator is653. The exponent in the result is384. The exponent in the numerator is unknown5. The properties of exponents apply, specifically the quotient of powers property which states that for any real numbers a, m, and n, a^(m)/a^(n) = a^(m-n)

STEP 2

We can use the quotient of powers property to simplify the left side of the equation. This property states that for any real numbers a, m, and n, a^(m)/a^(n) = a^(m-n).
$\frac{e^{?}}{e^{65}} = e^{?-65}$

STEP 3

Now, we can set the simplified left side of the equation equal to the right side of the equation.
$e^{?-65} = e^{38}$

STEP 4

Since the bases are the same (both are e), we can set the exponents equal to each other.
$?-65 =38$

STEP 5

olve for the unknown exponent by adding65 to both sides of the equation.
$? =38 +65$

STEP 6

Calculate the value of the unknown exponent.
$? =38 +65 =103$ The missing exponent is103.

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QuestionFind the missing exponent in $\frac{e^{?}}{e^{65}}=e^{38}$ .

Studdy Solution

STEP 1

STEP 2

We can use the quotient of powers property to simplify the left side of the equation. This property states that for any real numbers a, m, and n, a^(m)/a^(n) = a^(m-n).
$\frac{e^{?}}{e^{65}} = e^{?-65}$

STEP 3

Now, we can set the simplified left side of the equation equal to the right side of the equation.
$e^{?-65} = e^{38}$

STEP 4

Since the bases are the same (both are e), we can set the exponents equal to each other.
$?-65 =38$

STEP 5

olve for the unknown exponent by adding65 to both sides of the equation.
$? =38 +65$

STEP 6

Calculate the value of the unknown exponent.
$? =38 +65 =103$ The missing exponent is103.

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QuestionFind the missing exponent in e?e65=e38\frac{e^{?}}{e^{65}}=e^{38}e65e?​=e38.

Studdy Solution

STEP 1

STEP 2

We can use the quotient of powers property to simplify the left side of the equation. This property states that for any real numbers a, m, and n, a^(m)/a^(n) = a^(m-n).e?e65=e?−65\frac{e^{?}}{e^{65}} = e^{?-65}e65e?​=e?−65

STEP 3

Now, we can set the simplified left side of the equation equal to the right side of the equation.e?−65=e38e^{?-65} = e^{38}e?−65=e38

STEP 4

Since the bases are the same (both are e), we can set the exponents equal to each other.?−65=38?-65 =38?−65=38

STEP 5

olve for the unknown exponent by adding65 to both sides of the equation.?=38+65? =38 +65?=38+65

STEP 6

Calculate the value of the unknown exponent.?=38+65=103? =38 +65 =103?=38+65=103The missing exponent is103.

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QuestionFind the missing exponent in $\frac{e^{?}}{e^{65}}=e^{38}$ .

We can use the quotient of powers property to simplify the left side of the equation. This property states that for any real numbers a, m, and n, a^(m)/a^(n) = a^(m-n).
$\frac{e^{?}}{e^{65}} = e^{?-65}$

Now, we can set the simplified left side of the equation equal to the right side of the equation.
$e^{?-65} = e^{38}$

Since the bases are the same (both are e), we can set the exponents equal to each other.
$?-65 =38$

olve for the unknown exponent by adding65 to both sides of the equation.
$? =38 +65$

Calculate the value of the unknown exponent.
$? =38 +65 =103$ The missing exponent is103.