1) 4 sqrt x^3 =====> 4x^3/2 =====> 4x sqrt x
Steps:
4 sqrt x^3
sqrt x^3
x^3/2
Answer ======> 4x^3/2 =====> 4x sqrt x
2): 1 / x^ -1 =====> x
Steps:
1 / x^ -1
Apply exponent rule:
a^ -1 = 1 / a
x^ - 1 = 1 / x
1 / 1 / x
Apply fraction rule:
1 / b / c = c / b
x / 1
Apply Rule:
a / 1 = a
Answer ========> x
3): 10 sqrt x^5 * x^4 * x^2 = 10^17/2 ====> 100000000 * 10.5 (Decimal: 316227766 ).
Steps:
10 sqrt x^5 * x^4 * x^2
Apply exponent rule:
a^b * a^c = a^b + c
x^4x^2 = x^4 + 2 = x^6
10x^6 sqrt x^5
sqrt x^5 = x^5/2
10x^6x^5/2
Apply exponent rule:
a^b * a^c = a^b + c
x^6x^5/2 = x^5/2 + 6 = x^17/2
Answer ====> 10x^17/2 ==> 100000000 * 10.5 (Decimal: 316227766 ).
4): x^1/3 * x^1/3 * x^1/3 = x^3 / 27 ======> x^1/9
Steps:
x^1/3 * x^1/3 * x^1/3
Apply rule:
a^1 = a
x^1 = x
x/3 * x/3 * x/3
Multiply fractions:
a/b * c/d = a/b * c/d
xxx / 3*3*3
Multiply numbers:
3*3*3 = 27
Answer =========> x^3 / 27 =======> x^1/9
Hope that helps!!!! : )
