Question

11. Simplify (6x^-2)^2 (0.5x)^4 Show your work

Answer 1

The simplified form of ${\left( {6{x^{ - 2}}} \right)^2}{\left( {0.5x} \right)^4}$ is $\boxed{\frac{9}{4}{\text{ or 2}}{\text{.25}}}.$

Further explanation:

Given:

The expression is ${\left( {6{x^{ - 2}}} \right)^2}{\left( {0.5x} \right)^4}.$

Explanation:

The expression ${\text{A}} = {\left( {6{x^{ - 2}}} \right)^2}{\left( {0.5x} \right)^4}.$

Solve the given expression to obtain the simplified form.

$\begin{aligned}{\text{A}} &= {\left( {6{x^{ - 2}}} \right)^2}{\left( {0.5x} \right)^4}\\&= {6^2}{x^{ - 2 \times 2}} \times \frac{1}{{{2^4}}}{x^4}\\&= \frac{{36}}{{{x^4}}} \times \frac{1}{{16}}{x^4}\\&= \frac{{36{x^4}}}{{16{x^4}}}\\\end{aligned}$

Further solve the above equation.

$\begin{aligned}{\text{A}}&= \frac{{36{x^4}}}{{16{x^4}}}\\&= \frac{9}{4}\\&= 2.25\\\end{aligned}$

The simplified form of ${\left( {6{x^{ - 2}}} \right)^2}{\left( {0.5x} \right)^4}$ is $\boxed{\frac{9}{4}{\text{ or 2}}{\text{.25}}}.$

Learn more:

1. If the clothing maker bought 500 m2 of this fabric, how much money did he lose? use 1tepiz=0.625dollar and 0.9144m=1yard brainly.com/question/2479097.
2. Suppose that you find the volume of all the oceans to be 1.4×109km3 in a reference book. to find the mass, you can use the density of water, also found in this reference book, but first you must convert the volume to cubic meters. what is this volume in cubic meters? brainly.com/question/1446243.

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Polynomial

Keywords: simplified, exponents, power, $6x^-2$, work, exponents and power, expression.

Answer 2

Hope this helps you.