Answer:
1. x⁴³/³⁵
2. 1/x⁶
3. x⁴/2
Step-by-step explanation:
1. ⁷√x³. ⁵√x⁴
The above expression can be simplified as follow:
Recall:
ᵐ√aⁿ = aⁿ/ᵐ
⁷√x³ × ⁵√x⁴ = x³/⁷ × x⁴/⁵
Recall:
aⁿ × aᵐ = aⁿ⁺ᵐ
x³/⁷ × x⁴/⁵ = x⁽³/⁷ ⁺ ⁴/⁵⁾ = x⁴³/³⁵
Therefore,
⁷√x³. ⁵√x⁴ = x⁴³/³⁵
2. x¯³ / x⁵x¯²
The above expression can be simplified as follow:
Recall:
aⁿ × aᵐ = aⁿ⁺ᵐ
x⁵x¯² = x⁵ ⁺ ⁽¯²⁾ = x⁵ ¯ ² = x³
Thus,
x¯³ / x⁵x¯² = x¯³ / x³
Recall:
aⁿ / aᵐ = aⁿ ¯ ᵐ
x¯³ / x³ = x¯³ ¯ ³ = x¯⁶
Recall
a¯ⁿ = 1/aⁿ
x¯⁶ = 1/x⁶
Therefore,
x¯³ / x⁵x¯² = 1/x⁶
3. 5(x⁴)³ / 10x⁸
The above expression can be simplified as follow:
Recall:
(aⁿ)ᵐ = aⁿ×ᵐ
5(x⁴)³ / 10x⁸ = 5x¹² / 10x⁸
Recall:
aⁿ / aᵐ = aⁿ ¯ ᵐ
5x¹² / 10x⁸ = (5/10)x¹² ¯ ⁸ = 1/2 x⁴ = x⁴/2
Therefore,
5(x⁴)³ / 10x⁸ = x⁴/2
The number is 6. The equation would be 8x - 12 = 36. You add over the 12 to the 36 to get 48. Then when you do 8x divided by 48, you get x = 6. Therefore, the number the problem is asking for is 6.
C. i have only seen this method on checks
Answer:
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The answer is root of 27 and 38
square root of 24 = sqrt 4 × sqrt 6 = 2 root 6
square root of 32 = sqrt 16 × sqrt 2 = 4 root
square root of 27 = sqrt 9 × sqrt 3
square root of 38 = sqrt 19 × sqrt 2
square root of 27 and 38 can't be simplified