Math Problem Statement

r^8s^-5t^0/r^0s^-5t^6

Solution

To simplify the expression:

r8s5t0r0s5t6\frac{r^8 s^{-5} t^0}{r^0 s^{-5} t^6}

Step-by-step solution:

  1. Simplify t0t^0: Since t0=1t^0 = 1, we can eliminate t0t^0 from the numerator: r8s5r0s5t6\frac{r^8 s^{-5}}{r^0 s^{-5} t^6}

  2. Simplify each variable by subtracting exponents:

    • For rr, subtract the exponents: r8r0=r80=r8\frac{r^8}{r^0} = r^{8 - 0} = r^8

    • For ss, subtract the exponents: s5s5=s5(5)=s0=1\frac{s^{-5}}{s^{-5}} = s^{-5 - (-5)} = s^0 = 1 So, ss cancels out entirely.

    • For tt, since there is no tt in the numerator, just keep t6t^6 in the denominator: 1t6\frac{1}{t^6}

Final simplified expression:

r8t6\frac{r^8}{t^6}

Would you like more details on any of these steps?


Here are 5 related questions:

  1. How do you handle terms like t0t^0 and r0r^0 in expressions?
  2. What happens when both numerator and denominator have the same exponent for a variable?
  3. How would you simplify ama0\frac{a^m}{a^0}?
  4. What happens when the exponents cancel out for a variable, like s5/s5s^{-5}/s^{-5}?
  5. Can you simplify expressions like xaybxcyd\frac{x^a y^b}{x^c y^d}?

Tip: When you encounter x0x^0 in an expression, remember it always equals 1 as long as x0x \neq 0.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Simplifying Rational Expressions

Formulas

Exponent rule: a^m / a^n = a^(m-n)
Zero exponent rule: a^0 = 1

Theorems

Properties of Exponents
Simplification of Rational Expressions

Suitable Grade Level

Grades 8-10