Exercise 1 Page 352

Let's simplify the left-hand side of the given expression. The exponent we get after simplifying will be our answer.

x^(5/3)* x^(- 1)*sqrt(x)/x^(- 2)* x^0

RootToPowSL

sqrt(a)=a^(1/n)

x^(5/3)* x^(- 1)* x^(1/3)/x^(- 2)* x^0

▼

Simplify numerator

MultPow

a^m*a^n=a^(m+n)

x^(5/3-1+1/3)/x^(- 2)* x^0

1=a/a

x^(5/3-3/3+1/3)/x^(- 2)* x^0

AddSubFrac

Add and subtract fractions

x^(3/3)/x^(- 2)* x^0

QuotOne

a/a=1

x^1/x^(- 2)* x^0

▼

Simplify denominator

MultPow

a^m*a^n=a^(m+n)

x^1/x^(- 2+0)

AddTerms

Add terms

x^1/x^(- 2)

▼

Simplify

DivPow

a^m/a^n= a^(m-n)

x^(1-(- 2))

SubNeg

a-(- b)=a+b

x^(1+2)

AddTerms

Add terms

x^3