simplify: x^675/x^453

Answer 1

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 2

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

Answer 3

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 4

x^38/x^65=e^?

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

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