How do you solve variables with exponents?

How do you solve variables with exponents?

For example, to solve 2x – 5 = 8x – 3, follow these steps:

1. Rewrite all exponential equations so that they have the same base. This step gives you 2x – 5 = (23)x – 3.
2. Use the properties of exponents to simplify. A power to a power signifies that you multiply the exponents.
3. Drop the base on both sides.
4. Solve the equation.

How do you simplify polynomial fractions with exponents?

To simplify a fraction with a factorable polynomial in the numerator and the denominator, factor the polynomial in the numerator and the denominator. Then reduce the fraction to lowest terms by canceling out any monomials or polynomials that exist in both the numerator and denominator.

How do you solve fractions with unknown variables?

You can solve for an unknown value x in algebraic equations containing fractions using a few simple steps.

1. Step One: Cross Multiply the Fraction.
2. Step Two: Solve the Equation.
3. Step Three: Reduce the Fraction.

How do you change mixed numbers into improper fractions?

Answer: To turn a mixed number into an improper fraction, multiply the whole number with the denominator of the proper fraction. Add the numerator of the proper fraction to this product to obtain the numerator of the improper fraction.

How do you divide fractions with exponents?

To divide exponents in the same base, subtract the exponent on the second base (the denominator in a fraction) from the one on the first (the numerator in a fraction). The general rule is: x a ÷ x b = x (a − b) You can only use this rule when the base is the same.

How do you simplify variables with fractions?

Simplifying Complex Fractions Containing Variable Terms When possible, use the inverse multiplication method above. To be clear, virtually any complex fraction can be simplified by reducing its numerator and denominator to single fractions and multiplying the numerator by the inverse of the denominator.

How do you simplify an expression with a fraction?

Simplifying Complex Expressions Add like variable terms. Simplify numerical fractions by dividing or “canceling out” factors. In variable fractions, cancel out variable factors. Multiply parenthetical terms by their constants. Simplify by factoring.

What are the rules when adding exponents?

The first rule to remember when adding with exponents is the order of operations: parenthesis, exponents, multiplication, division, addition, subtraction. This order of operations places exponents second in the solving scheme. So if you know both the base and the exponent, solve them before moving on.