Question

Challenge: find values of x, y and z so that each of the expression x², y², and z⁶ has a value of 64.

Short answer

x = 8; y = 8 and z = 2

Step-by-step solution

– Explanation of the exponent formula

${\text{a}}^{\text{x}}\to$a is the base and x is exponent.

The power is the result of repeated multiplication of the same factor.

The expressionsa^xthis means that a has been used as a factor x times.

Write the product 5 · 5 · 5 · 5in exponent and evaluate

Example: Write the product $5 · 5 · 5 · 5$in exponent.

Rule: ${\text{a}}^{\text{x}}\to$a is called base and x is power.

For:$5 · 5 · 5 · 5$:the base a = 5 and multiplied by 4 times.

In repeated multiplication: $5 · 5 · 5 · 5$in exponent form $5^4$

Evaluate: $5^4 = 5 · 5 · 5 · 5 = 625$

Find the values of x, y and z so that each expression x2, y2 and z6 has a value of 64.

Let we try with trial and error method. 64 is an even number and all the exponents are even number, so we will consider x, y and z as multiple of 2

x, y and z all are equal to 2

$\begin{array}{l}{x}^2=2·2=4\\ y^2=2·2=4\\ z^6=2·2·2·2·2·2=64\end{array}$

We already calculated $z^6=64$

Now let x = y = 4

$x^2=4 · 4=16$&$y^2=4 · 4=16$

Let x = y = 8

$x^2=8 · 8=64 \& y^2=8 · 8=64$

We can write x = 8, y = 8 and z = 2 has a value of 64.