Divide Mixed Numbers By Fractions Calculator With Exponents

Division Formula:

\[ (m \frac{n}{o})^k \div (\frac{a}{b})^l = \left(\frac{m \times o + n}{o}\right)^k \times \left(\frac{b}{a}\right)^l \]

Whole Number (m):

Numerator (n):

Denominator (o):

Exponent (k):

Fraction Numerator (a):

Fraction Denominator (b):

Exponent (l):

Result:

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1. What is This Calculator?

This calculator divides mixed numbers by fractions, both raised to exponents. It converts the mixed number to an improper fraction, applies the exponents, and performs the division by multiplying by the reciprocal.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ (m \frac{n}{o})^k \div (\frac{a}{b})^l = \left(\frac{m \times o + n}{o}\right)^k \times \left(\frac{b}{a}\right)^l \]

Where:

\( m \) — Whole number part
\( n \) — Numerator of mixed number fraction
\( o \) — Denominator of mixed number fraction
\( k \) — Exponent for the mixed number
\( a \) — Numerator of divisor fraction
\( b \) — Denominator of divisor fraction
\( l \) — Exponent for the divisor fraction

3. Mathematical Explanation

Step 1: Convert mixed number to improper fraction: \( m \frac{n}{o} = \frac{m \times o + n}{o} \)
Step 2: Apply exponents to numerator and denominator
Step 3: Division by fraction becomes multiplication by reciprocal
Step 4: Multiply the two resulting terms

4. Using the Calculator

Tips: Enter all required values. Denominators cannot be zero. Exponents can be any real number (fractional exponents allowed).

5. Frequently Asked Questions (FAQ)

Q1: Can I use negative exponents?
A: Yes, negative exponents are allowed and will create reciprocals of the base.

Q2: What if my mixed number is negative?
A: Include the negative sign with the whole number (m).

Q3: Can I use decimal values?
A: Yes, but for mixed numbers, it's better to use whole numbers for m, n, and o.

Q4: What if I get an error?
A: Check that denominators (o, b) aren't zero and that you're not raising zero to a negative power.

Q5: How precise is the result?
A: Results are shown to 4 decimal places for clarity.