Posts tagged exponents
How to simplify powers of fractions and fractional exponents

There are two ways that fractions get involved in exponents. The first is when the exponent itself is a fraction. The second is when the base is a fraction, and we’re raising that fractional base to an exponent. This lesson will cover how to find the power of a fraction as well as introduce how to work with fractional exponents.

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Exponents on negative bases

There are two cases to think of when you’re simplifying powers of negative bases. The first is when the base actually isn’t negative at all, because there are no parentheses around the negative sign. In that case, we’ll apply the exponent to the positive base, and then apply the negative sign afterwards. The second is when we have parentheses around the negative sign, in which case the exponent applies to the base and its negative sign.

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Exponent rules

When we want to find the sum or difference of two exponential expressions, they must be “like terms,” meaning that they must have the same base and the same exponent; otherwise, we can’t add or subtract them. Multiplication and division of exponential expressions is a little different. When we multiply and divide, we need only the bases to be the same. We do not need the exponents to be the same.

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Quotient rule for exponents to simplify fractions

This is the rule we use when we’re dividing one exponential expression by another exponential expression. The quotient rule tells us that we have to subtract the exponent in the denominator from the exponent in the numerator, but the bases have to be the same.

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