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Juli2301 [7.4K]
2 years ago
5

What is the solution of (8x-8) 3/2=64 A. x=3 B. x=5 C x=13 D x=65

Mathematics
2 answers:
Stells [14]2 years ago
6 0

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}.

Learn more:

1. Learn more about unit conversion brainly.com/question/4837736

2. Learn more about non-collinear brainly.com/question/4165000

3. Learn more aboutbinomial and trinomialhttps://brainly.com/question/1394854

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.

kramer2 years ago
5 0

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.

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