Multiplying Monomials (Values and Variables) over Unit Fraction (Level 3)

This topic covers the skills of multiplying monomials, which include both values and variables, within the context of working with radicals and unit fractions. It is designed to strengthen understanding of radical expressions, specifically how to multiply and simplify them when placed over a unit fraction. Each question presents a different set of variables and powers, requiring the application of rules for multiplying radicals and simplifying the resulting expressions. This is a more advanced practice in dealing with radicals, aimed at students ready for higher-level algebraic operations.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

more
View

Radicals - Multiplying Monomials (Values and Variables) over Unit Fraction Worksheet

Mobius Math Academy logo
Radicals - Multiplying Monomials (Values and Variables) over Unit Fraction
1
A LaTex expression showing \frac{square root of 8 times square root of 99m{b to the power of 2 }}{1 over 4 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 6bsquare root of 22m
b A LaTex expression showing 6bsquare root of 22{m to the power of -1 }
c A LaTex expression showing 6bsquare root of 22
d A LaTex expression showing 24bsquare root of 22m
e A LaTex expression showing 96bsquare root of m
2
A LaTex expression showing \frac{square root of 12{n to the power of 3 {x} to the power of 2 } times square root of 28{n to the power of 3 {x} to the power of 4 }}{1 over 3 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 12{n} to the power of 3 {x} to the power of 3 square root of 21
b A LaTex expression showing 4{n} to the power of 2 {x} to the power of 3 square root of 21
c A LaTex expression showing 4{n} to the power of 3 {x} to the power of 2 square root of 21
d A LaTex expression showing 4{n} to the power of 3 {x} to the power of 3 square root of 21
3
A LaTex expression showing \frac{square root of 12{n to the power of 3 {b} to the power of 3 } times square root of 48n{b to the power of 2 }}{1 over 5 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 120{n} to the power of 2 {b} to the power of 2 square root of b
b A LaTex expression showing 600{n} to the power of 2 {b} to the power of 2 square root of b
c A LaTex expression showing 24{n} to the power of 2 {b} to the power of 2 square root of b
d A LaTex expression showing 24{n} to the power of 2 {b} to the power of 3
4
A LaTex expression showing \frac{square root of 32{r to the power of 4 {n} to the power of 3 } times square root of 63{r to the power of 2 {n} to the power of 2 }}{1 over 3 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 36{r} to the power of 3 {n} to the power of 2 square root of 14n
b A LaTex expression showing 12{r} to the power of 2 {n} to the power of 2 square root of 14n
c A LaTex expression showing 12{r} to the power of 3 {n} to the power of 3 square root of 14
d A LaTex expression showing 12{r} to the power of 3 {n} to the power of 2 square root of 14n
e A LaTex expression showing {r} to the power of 3 {n} to the power of 2 square root of n
5
A LaTex expression showing \frac{square root of 80{m to the power of 2 } times square root of 27{m to the power of 3 {r} to the power of 4 }}{1 over 5 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 12{m} to the power of 2 {r} to the power of 2 square root of 15mr
b A LaTex expression showing 12{m} to the power of 3 {r} to the power of 2 square root of 15
c A LaTex expression showing 60{m} to the power of 2 {r} to the power of 2 square root of 15m
d A LaTex expression showing 300{m} to the power of 2 rsquare root of 15mr
e A LaTex expression showing 300{m} to the power of 2 {r} to the power of 2 square root of 15m
6
A LaTex expression showing \frac{square root of 12{m to the power of 4 {x} to the power of 4 } times square root of 117{x to the power of 2 }}{1 over 5 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 150{m} to the power of 2 {x} to the power of 3
b A LaTex expression showing 30{m} to the power of 2 {x} to the power of 3 square root of 39
c A LaTex expression showing 150{m} to the power of 2 {x} to the power of 3 square root of 39
d A LaTex expression showing 6{m} to the power of 2 {x} to the power of 3
e A LaTex expression showing 12{m} to the power of 2 {x} to the power of 3 square root of 39
7
A LaTex expression showing \frac{square root of 175{r to the power of 2 {p} to the power of 4 } times square root of 18{p to the power of 3 }}{1 over 3 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 15r{p} to the power of 3 square root of 14
b A LaTex expression showing 15{r} to the power of 2 {p} to the power of 3 square root of 14p
c A LaTex expression showing 45r{p} to the power of 3 square root of 14p
d A LaTex expression showing 15r{p} to the power of 3 square root of 14p
8
A LaTex expression showing \frac{square root of 27{p to the power of 2 {m} to the power of 4 } times square root of 32}{1 over 2 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 48{m} to the power of 2 square root of 6
b A LaTex expression showing 24p{m} to the power of 2 square root of 6
c A LaTex expression showing 12p{m} to the power of 2 square root of 6
d A LaTex expression showing 60p{m} to the power of 2 square root of 6
e A LaTex expression showing 12p{m} to the power of 2