Chapter 12, Problem 14CLR

To determine

To Evaluate: The simplified value of the expression ${\left(5x^3{y}^2\right)}^2{\left(3x^4{y}^3\right)}^2$ .

Answer to Problem 14CLR

The value of the expression ${\left(5x^3{y}^2\right)}^2{\left(3x^4{y}^3\right)}^2$ is $225x^{14}{y}^{10}$ .

Explanation of Solution

Given information:

The expression is ${\left(5x^3{y}^2\right)}^2{\left(3x^4{y}^3\right)}^2$ .

Formula used:

Square of any expression is same as multiplication of the expression with itself. That is,

  $x^2=x\times x$

When a algebraic term is multiply by another algebraic term power of same variable added and

the numerical coefficients multiply together.

Example-:

  $\begin{array}{c}5x^{2}y\times \left(-7x\right)=-35xy{}^{1+0}\\ =-35x^3{y}^1\end{array}$

Calculation:

Consider the expression is ${\left(5x^3{y}^2\right)}^2{\left(3x^4{y}^3\right)}^2$ .

Recall that square of any expression is same as multiplication of the expression with itself. That is,

  $x^2=x\times x$

Use it,

  ${\left(5x^3{y}^2\right)}^2{\left(3x^4{y}^3\right)}^2=\left(5x^3{y}^2\right)\left(5x^3{y}^2\right)\left(3x^4{y}^3\right)\left(3x^4{y}^3\right)$

Again recall that when a algebraic term is multiply by another algebraic term power of same

variable added and the numerical coefficients multiply together.

Apply it,

  $\begin{array}{c}\left(5x^3{y}^2\right)\left(5x^3{y}^2\right)\left(3x^4{y}^3\right)\left(3x^4{y}^3\right)=\left(5\times 5x^{3+3}{y}^{2+2}\right)\left(3\times 3x^{4+4}{y}^{3+3}\right)\\ =25xy{}^4\times 9x^8{y}^6\\ =25\times 9x^{6+8}{y}^{4+6}\\ =225x^{14}{y}^{10}\end{array}$

Thus, the value of the expression ${\left(5x^3{y}^2\right)}^2{\left(3x^4{y}^3\right)}^2$ is $225x^{14}{y}^{10}$ .