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Perplex
Perplex
  • Dashboard
Topics
Exponents & LogarithmsRounding & ErrorSequences & SeriesCounting & BinomialsProof and Reasoning
Cartesian plane & linesQuadraticsFunction TheoryTransformations & asymptotes
2D & 3D GeometryTrig equations & identities
ProbabilityDescriptive StatisticsBivariate StatisticsDistributions & Random Variables
DifferentiationIntegration
Calculator Skills
Review VideosFormula BookletAll Study Sets
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Perplex

Exponents & Logarithms (Lesson 2/4)

Radicals and Roots

1 / 28

Discussion

So far, we have only seen integer exponents, but fractional exponents exist too. Using your knowledge of exponential laws, determine the value of ​6431​.​

Solution:

We want to find ​641/3. Recall the law of exponents

​
(an)m=anm
​

and set

​
x=641/3.
​

Then

​
x3=(641/3)3=64(1/3)â‹…3=641=64
​

so ​x​ is a number whose cube is 64. Since ​43=64, we conclude

​
641/3=4.
​


1 free

Exponents & Logarithms (Lesson 2/4)

Radicals and Roots

1 / 28

Discussion

So far, we have only seen integer exponents, but fractional exponents exist too. Using your knowledge of exponential laws, determine the value of ​6431​.​

Solution:

We want to find ​641/3. Recall the law of exponents

​
(an)m=anm
​

and set

​
x=641/3.
​

Then

​
x3=(641/3)3=64(1/3)â‹…3=641=64
​

so ​x​ is a number whose cube is 64. Since ​43=64, we conclude

​
641/3=4.
​


1 free