How to calculate the degree?

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How to calculate the degree?

Raise the number a to the power n means that you need to multiply the number a by a n times. This is understandable if a is an integer. But there are fractional or negative degrees. How many times do you need to multiply a number in these cases? How to calculate the fractional power of a number is written in the article How to raise to a fractional power? | We give examples of such calculations. Consider examples for all exponentiation options.

How to calculate a degree with a whole indicator

Computing a degree with a positive integer exponent

When raising any number to the power of 0, 1 is always obtained:

  • 3*0 = 1

When raising a negative number to the power of 0, it will be -1:

  • -3*0 = -1×3*0 = -1×1 = -1

When raising a number to the power of 1, the number remains unchanged:

  • 3*1 = 3
  • -3*1 = -3

When raising any number to an even power, a positive number is always obtained:

  • 3² = 9
  • -3² = 9

When raised to an odd degree, the sign of the number remains unchanged:

  • 3³ = 27
  • -3³ = -27

Calculating a degree with a negative integer exponent

The minus in the exponent changes the numerator and denominator of the number:

  • 5*(-1) = 1/5 = 0,2
  • -5*(-1) = -1/5 = -0,2
  • (2/3)*(-1) = (3/2)*1 = 3/2
  • 5*(-2) = (1/5²) = 1/25 = 0,04

When a negative number is raised to a negative degree, the even degree rule is preserved:

  • -5*(-2) = (1/-5)² = 1/25 = 0,04
  • -5*(-3) = (1/-5)³ = -1/125 = -0,016

How to calculate the power of a number with a fractional exponent

The fractional exponent indicates that a number must be raised to a power equal to the numerator of the indicator and the root of a degree equal to the denominator must be extracted:

  • 64*(1/2) = √64 = 8
  • 8*(⅔) = ³√ 8² = ³√64 = 4
  • 4*(3/2) = ²√4³ = ²√64 = 8
  • 4*(-1/2) = ¼*(1/2) = 1/²√4 = ½ = 0,5
  • 25*0,5 = 25*(½) = ²√25 = 5

Mixed fraction in the exponent must be turned into the wrong:

  • 16*(1½) = 16*(3/2) = ²√(16)³ = 4³ = 64

Decimal fraction must be converted to simple.

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