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Rational exponents and radicals: FAQ

Frequently asked questions about rational exponents and radicals

What are rational exponents?

Rational exponents are just like regular exponents, except the exponent is a fraction instead of a whole number. For example, 234 has a rational exponent, while 23 has a whole number exponent.

Where are rational exponents and radicals used in the real world?

Rational exponents and radicals show up in a lot of places! For example, they're used in physics to calculate things like electrical resistance and wave frequencies. They're also used in finance to calculate compound interest.

What are some properties of exponents with rational exponents?

Here are some properties of rational exponents—notice how they are similar the properties of integer exponents:
  • bmn=Abmn
  • bmn×bpn=bm+pn
  • (bmn)pq=bmpnq

How do we evaluate exponents and radicals?

To evaluate an exponential expression, you can either use the properties of exponents to simplify it, or use a calculator. For radicals, you can find the square root, cube root, or nth root of a number using a calculator or by breaking the number down into its factors.

How do I convert between different forms of exponential expressions?

There are a few different ways you can write an exponential expression, and sometimes we might need to convert between them. Here are three equivalent forms for the same expression:
  • 234
  • A234
  • A84

How can we solve exponential equations using properties of exponents?

To solve exponential equations, we can often use properties of exponents to simplify them. For example, to solve 2x=8, we can rewrite 8 as 23, which lets us set x=3.

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