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7^5 times 4^5 is equivalent to (7 times 4)^5, which is 28^5. You could either leave your answer in this format or evaluate 28^5: 17210368.
(153^2)^7 is best done using the rule of exponents (x^a)^b = x^(ab). Multiply the exponents 2 and 7 together: (153^2)^7 = 153^(2*7) = 153^14.
(10^5)(4^5) has two factors, both of which have the exponent 5. We can rewrite this expression as (10*4)^5, which equals 40^5. No, this is not equal to 14^5!
2/5: 4/10 8/20 16/40 32/80 64/160 128/320
5/9: 10/18 20/36 40/72 80/144 160/288 320/576
<span>a/b = 3/5 ----- a = (3b)/5
a + b = 136 --- (3b)/5 + b = 136
3b + 5b = 680
8b = 680
b = 85
a = (3b)/5 = (3 * 85)/5 = 51
a = 85 and b = 51</span>
The expressions with radicals which are variables and numbers raised to a fractional indices are simplified as follows.
13. √(9·x) = 3·√x
14. √(4·y) = 2·√y
15. √(8·x²) = 2·x·√2
16. √(9·x²) = 3·x
17. √(3·x²) = x·√3
18. √(5·y²) = y·√5
19. √(13·x²) = x·√(13)
20. √(29·y²) = y·√(29)
21. √(64·y²) = 8·y
22. √(125·a²) = 5·a·√5
23. ∛(16) = 2·∛2
24. √(50·a²·b) = 5·a·√(2·b)
<h3>What are radicals expressions?</h3>
A radical expression is one that contains the radical (square root or nth root) sign, √.
13. √(9·x)
√(9·x) = √(3²·x) = 3·√x
14. √(4·y)
√(4·y) = √(2²·y) = 2·√y
15. √(8·x²)
√(8·x²) = √(4 × 2·x²) = √(2² × 2·x²)
√(2² × 2·x²) = √(2²·x² × 2) = 2·x·√2
16. √(9·x²)
√(9·x²) = √(3²·x²) = 3·x
17. √(3·x²)
18. √(5·y²)
√5 × √(y²) = √5 × y = y·√5
19. √(13·x²)
√(13·x²) = √(13) × √x² = √(13) × x = x·√(13)
20. √(29·y²)
√(29·y²) = √(29) × √(y²) = √(29) × y = y·√(29)
21. √(64·y²)
√(64·y²) = √(8²·y²) = √(8²) × √(y²) = 8 × y = 8·y
22. √(125·a²)
√(125·a²) = √(25 × 5 × a²) = √(25) × √5 × √(a²) = 5 × √5 × a
5 × √5 × a = 5·a·√5
23. ∛(16)
∛(16) = ∛(16) = ∛(8 × 2) = ∛(2³ × 2) = 2·∛2
24. √(50·a²·b)
√(50·a²·b) = √(25 × 2 × a² × b) = √(5² × 2 × a² × b) = √(5² × a² × 2 × b)
√((5² × a²) × 2 × b) = 5·a·√(2·b)
Learn more about simplifying expressions with radicals here:
brainly.com/question/13114751
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