Question

simplify: x^675/x^453

Answer 1

what is the missing exponent in the following equation?
e^?/e^65=e^38

Answer 2

x^38/x^65=e^?

Answer 3

To simplify the expression \( \frac{x^{675}}{x^{453}} \), you can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).

Applying this property:

\[
\frac{x^{675}}{x^{453}} = x^{675 - 453}
\]

Now, subtract the exponents:

\[
675 - 453 = 222
\]

So, the simplified expression is:

\[
x^{222}
\]

Answer 4

To find the missing exponent in the equation

\[
\frac{e^{?}}{e^{65}} = e^{38},
\]

you can use the property of exponents that states

\[
\frac{e^a}{e^b} = e^{a - b}.
\]

Applying this to the left side of the equation:

\[
\frac{e^{?}}{e^{65}} = e^{? - 65}.
\]

Setting this equal to the right side of the equation gives:

\[
e^{? - 65} = e^{38}.
\]

Since the bases are the same, you can set the exponents equal to each other:

\[
? - 65 = 38.
\]

Now, solve for the missing exponent:

\[
? = 38 + 65 = 103.
\]

Thus, the missing exponent is

\[
\boxed{103}.
\]

Answer 5

To simplify the expression \( \frac{x^{38}}{x^{65}} \), you can use the property of exponents that states

\[
\frac{a^m}{a^n} = a^{m-n}.
\]

Applying this property:

\[
\frac{x^{38}}{x^{65}} = x^{38 - 65} = x^{-27}.
\]

Now, the equation can be rewritten as:

\[
x^{-27} = e^{?}.
\]

At this point, to express \( x^{-27} \) in terms of \( e \), you can use the natural logarithm and the fact that \( x = e^{\ln(x)} \):

\[
x^{-27} = e^{-27 \ln(x)}.
\]

Therefore, we can set:

\[
e^{?} = e^{-27 \ln(x)}.
\]

This gives us:

\[
? = -27 \ln(x).
\]

So, the answer is

\[
\boxed{-27 \ln(x)}.
\]