Simplify this expression using the Quotient Rule of Integer Exponents; t^400 over t^100

Answer 1

To simplify the expression \(\frac{t^{400}}{t^{100}}\) using the Quotient Rule of Integer Exponents, we can apply the rule which states:

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

In this case, \(a = t\), \(m = 400\), and \(n = 100\). Therefore, we subtract the exponents:

\[ \frac{t^{400}}{t^{100}} = t^{400 - 100} = t^{300} \]

Thus, the simplified expression is:

\[ t^{300} \]

Answer 2

what is the Quotient Rule of Integer Exponents:

Answer 3

The Quotient Rule of Integer Exponents states that when you divide two expressions that have the same base, you subtract the exponent of the denominator from the exponent of the numerator. This can be expressed formally as follows:

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

Where:

• \(a\) is the base (and must be non-zero),
• \(m\) is the exponent of the numerator,
• \(n\) is the exponent of the denominator.

Example: For instance, if you have \(\frac{x^5}{x^2}\), according to the Quotient Rule, you would simplify it as follows:

\[ \frac{x^5}{x^2} = x^{5-2} = x^3 \]

The rule applies as long as the base \(a\) is the same in both the numerator and the denominator. If the bases are different, the Quotient Rule does not apply.

Answer 4

so t^400 over t^100 is simplified to t^300?

Answer 5

Yes, exactly! The expression \(\frac{t^{400}}{t^{100}}\) simplifies to \(t^{300}\) by applying the Quotient Rule of Integer Exponents.

Here's a recap of the step:

\[ \frac{t^{400}}{t^{100}} = t^{400 - 100} = t^{300} \]

So the simplified form is indeed \(t^{300}\).