Question

What is the solution of (8x-8) 3/2=64

A. x=3
B. x=5
C x=13
D x=65

Answer 1

Answer:

A. $x=3$

Step-by-step explanation:

We have been given an equation $(8x-8)^{\frac{3}{2}}=64$ and we are asked to find the solution for our given equation.

First of all let us raise both sides of our equation to 2/3 power.

$((8x-8)^{\frac{3}{2}})^{\frac{2}{3}}=(64)^{\frac{2}{3}}$

Using the exponent property $(a^b)^c=a^{b*c}$ we will get,

$(8x-8)^{\frac{3}{2}\times \frac{2}{3}}=(64)^{\frac{2}{3}}$

$(8x-8)^1=(64)^{\frac{2}{3}}$

Using exponent property $a^{\frac{m}{n}}=\sqrt[n]{a^m}$ we will get,

$(8x-8)=\sqrt[3]{64^2}$

$8x-8=\sqrt[3]{4096}$

$8x-8=16$

$8x-8+8=16+8$

$8x=24$

Let us divide both sides of our equation by 8.

$\frac{8x}{8}=\frac{24}{8}$

$x=3$

Therefore, the solution for our given equation is 3 and option A is the correct choice.

Answer 2

The solution of the equation ${\left( {8x - 8} \right)^{\dfrac{3}{2}}}= 64\: {\text{is}\: \boxed{x = 3}.$

Further explanation:

Given:

The exponent equation is ${\left( {8x - 8} \right)^{\dfrac{3}{2}}} = 64.$

Calculation:

The exponents are the powers on the numbers.

The rules of exponents are as follows,

1.$\boxed{\left( {{x^m}}\right)\times \left( {{x^n}}\right) = {x^{m + n}}}$

2. $\boxed{\dfrac{{{x^m}}}{{{x^n}}} = {x^{m - n}}}$

3. $\boxed{{{\left({{x^a}} \right)}^b} = {x^{a \times b}}}$

4. $\boxed{{x^{\dfrac{m}{n}}} = \sqrt[n]{{{x^m}}}}$

Solve the equation ${\left( {8x - 8}\right)^{\dfrac{3}{2}}} = 64$ to obtain the value of x.

$\begin{aligned}{\left({8x - 8} \right)^{\frac{3}{2}}}&= 64\\{\left({{{\left( {8x - 8} \right)}^{\frac{3}{2}}}} \right)^{\frac{2}{3}}}&= {\left( {64} \right)^{\frac{2}{3}}}\\8x - 8&= \sqrt[3]{{{{64}^2}}}\\8x - 8&=\sqrt[3]{{4096}}\\\end{aligned}$

Further solve the above equation.

$\begin{aligned}8x - 8&= 16\\8x &= 16 + 8\\8x&=24\\x&= \frac{{24}}{8}\\x&= 3\\\end{aligned}$

Hence, the solution of the equation ${\left( {8x - 8} \right)^{\dfrac{3}{2}}} = 64\:{\text{is}\:\boxed{x = 3}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponents

Keywords: Solution, ${\left( {8x - 8} \right)^{\dfrac{3}{2}}} = 64$, exponents, power, equation, power rule, exponent rule.