Radicals and Exponents Simplify the expression. x4(3x)2x3

Question

Radicals and Exponents Simplify the expression.  x4(3x)2x3

Bentley Leach · Accepted Answer

Procedure used:
The definition of a Rational Exponent is,
For any rational exponent m/n in lowest, where m and n are integers and $n > 0$ , we define
$a^{m / n} = (\sqrt[n]{a})^{m} or equivalently a^{m / n} = {\sqrt[n]{a}}^{m}$
If n is even, then we require that $a \geq 0$ .
$\sqrt{a} = b means b^{2} = a and b \geq 0$
This implies that $b = a^{\frac{1}{2}}$ and therefore
$\sqrt{a} = a^{\frac{1}{2}}$
According to the Zero and Negative Exponents rule, we can see that if $a \neq q 0$ is a real number and n is a positive integer, then
$a^{0} = 1 and a^{- n} = \frac{1}{a^{n}}$
From, the law of exponents, we know that
${(a b)}^{m} = a^{m} b^{m}$ .....(1)
$a^{m} a^{n} = a^{m + n}$ .....(2)
$\frac{a^{m}}{a^{n}} = a^{m - n}$ .....(3)
Calculation:
Using the Law of Exponents (1), (2) and (3), we get that
$\frac{x^{4} {(3 x)}^{2}}{x^{3}} = \frac{x^{4} (3^{2} x^{2})}{x^{3}}$
$= \frac{3^{2} x^{4 + 2}}{x^{3}}$
$= \frac{3^{2} x^{6}}{x^{3}}$
$= 9 x^{6 - 3}$
$= 9 x^{3}$
Answer:
The simplified form of the expression, $\frac{x^{4} {(3 x)}^{2}}{x^{3}} = 9 x^{3}$

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Radicals and Exponents Simplify the expression. frac{x^{4}(3x)^{2}}{x^{3}}

Answered question

Answer & Explanation

New Questions in Algebra II