3000⋅4300p

Reduce the expression 3000⋅4300 by cancelling the common factors.

Factor 300 out of 3000⋅4.

300(10⋅4)300p

Factor 300 out of 300.

300(10⋅4)300(1)p

Cancel the common factor.

300(10⋅4)300⋅1p

Rewrite the expression.

10⋅41p

10⋅41p

Divide 10⋅4 by 1.

10⋅4p

10⋅4p

Multiply 10 by 4.

40p

Rewrite 40p as 40p.

40p

Rewrite 40 as 22⋅10.

Factor 4 out of 40.

4(10)p

Rewrite 4 as 22.

22⋅10p

22⋅10p

Pull terms out from under the radical.

210p

210p

Multiply 210p by pp.

210p⋅pp

Multiply 210p and pp.

210ppp

Raise p to the power of 1.

210pp1p

Raise p to the power of 1.

210pp1p1

Use the power rule aman=am+n to combine exponents.

210pp1+1

Add 1 and 1.

210pp2

Rewrite p2 as p.

Use axn=axn to rewrite p as p12.

210p(p12)2

Apply the power rule and multiply exponents, (am)n=amn.

210pp12⋅2

Combine 12 and 2.

210pp22

Cancel the common factor of 2.

Cancel the common factor.

210pp22

Divide 1 by 1.

210pp1

210pp1

Simplify.

210pp

210pp

210pp

Combine using the product rule for radicals.

2p⋅10p

Move 10 to the left of p.

210pp

Simplify square root of ((3000*4)/300)/p