1a. 10. 24
1b. 125/243
2a. 0. 0048
2b. 32/3125
3a. 0. 64
3b. 0. 0031
4a. 2/5
4b. 48. 735
5a. 2. 36
5b. 1. 39
How to determine the values
1a. Given the values
(2/5)^2/(1/2)^6
Multiply both the numerator and denominator by the powers
⇒ [tex]\frac{\frac{4}{25} }{\frac{1}{64} }[/tex]
To find the common ration, multiply thus;
⇒ [tex]\frac{4}{25}[/tex] × [tex]\frac{64}{1}[/tex]
⇒ [tex]\frac{256}{25}[/tex]
= 10. 24
1b. (5/7)^2 × (5/7)^1
= [tex]\frac{25}{49}[/tex] × [tex]\frac{5}{7}[/tex]
= [tex]\frac{125}{343}[/tex]
= 125/243
2a. 0. 6^1 × 0. 2^3
= 0. 6 × 0. 008
= 0. 0048
2b. (2/5)^3 × (2/5)^2
= [tex]\frac{8}{125}[/tex] × [tex]\frac{4}{25}[/tex]
= [tex]\frac{32}{3125}[/tex]
= 32/ 3125
3a. 1^99 - 0. 6^2
= 1 - 0. 36
= 0. 64
3b. (0. 2 ) ^1 × (1/8)^2
= 0. 2 × 1/64
= 0. 2 × 0. 016
= 0. 0031
4a. (1/2)^2/ (5/8)^1
= [tex]\frac{\frac{1}{4} }{\frac{5}{8} }[/tex]
Take the inverse of the denominator
= [tex]\frac{1}{4}[/tex] × [tex]\frac{8}{5}[/tex]
= 2/5
4b. 7^2 - 0. 5^3
= 49 - 0. 125
= 48. 875
5a. 3^1 - 0. 8 ^2
= 3 - 0. 64
= 2. 36
5b. 0. 7^2 + 0. 9^1
= 0. 49 + 0. 9
= 1. 39
Learn more about index notation here:
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