Question

a.5³ * 3⁷ * 15-⁵ (linia to kreska ułamkowa pod nią powinno być 9-¹ * 3⁴ *25-¹)

b.2⁷ * 3⁸ (linia to kreska ułamkowa pod nią powinno być 9³ * 2⁵ )

c. [ 4 * 3-⁷ - 3⁷]⁰ (linia to kreska ułamkowa pod nią powinno być 2-2 * (1/4)²

d. [17 - 35⁴ : 25² * 7-³] : 0.01

Answer 1

Własności potęg

 

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a) [5³ * 3⁷ * 15]/[ 9-¹ * 3⁴ *25-¹)]=

=[5³ * 3⁷ * 3 * 5]/[(3²)⁻¹ * 3⁴ * (5²)⁻¹]=

=[5³⁺¹ * 3⁷⁺¹]/[3⁻²⁺⁴ * 5⁻²]=

=[5⁴ * 3⁸]/[3² * 5⁻²]=

=5⁴⁺² * 3⁸⁻²=

=5⁶ * 3⁶=

=(5*3)⁶=

=15⁶

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b) [2⁷ * 3⁸]/[9³ * 2⁵]=

=[2⁷ * 3⁸]/[(3²)³ * 2⁵]=

=[2⁷ * 3⁸]/[3⁶ * 2⁵]=

=2⁷⁻⁵ * 3⁸⁻⁶=

=2² * 3²=

=(2*3)²=

=6²=

=36

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c) [4 * 3-⁷ - 3⁷]⁰]/[2-2 * (1/4)²]=

=1/[2-2 * 1/16]=

=1/[2 - 1/8]=

=1/[15/8]=

=1 : 15/8=

=1* 8/15=

=8/15

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d) [17 - 35⁴ : 25² * 7-³] : 0.01=

=[17 - 5⁴ * 7⁴ : 5⁴ * 7⁻³] * 1/100=

=[17 - 5⁴⁻⁴ * 7⁴⁻³] * 1/100=

=[17 - 7] * 1/100=

=10 * 1/100=

=1/10