Order of Operations: Exponential Problems

Order of Operations: Exponential Problems

Exponents can be written in different forms. For example as:

• radicals
• fractions
• negatives
• logarithms
• polynomials
• etc.

Once you prioritize your order of operations acronym, you can prioritize the exponent accordingly, even in radical form.

Connect radicals to exponents

Radicals are generally rewritten as a fractional exponent when the fractional exponent (x) is 0 < x < 1. In this case:

This is like saying fractions can be rewritten as decimals. But, do your students understand this? If you teach scholars that radicals are included as a form of exponents, you can help prevent confusion when scholars see radicals while performing the order of operations.

Connect logarithms to exponents

Logarithmic form is another way of expressing the exponential form. The logarithmic form allows you to find the exponent of an equation. Therefore, finding the log of a number with a certain base allows you to find the exponent.

In the logarithmic form, the base “x” is located as a subscript next to log. You find the “log of a, base x” and find the “n” exponent.

In the exponential form, the “n” exponent is raised as the superscript above the “x” base. This equals the “a” power.

Connect Logarithms, radicals and exponents

Both radical and logarithmic forms have their place. They provide some shorthand methods of depicting exponents as both fractions and integers. These alternatives are widely used and are worth understanding.

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