Question

can someone show me the steps to solve (6x^-2)^2(0.5x)^4
I know the answer is 2.25

Answer 1

If you don't know the steps to this equation, how did you solve it?

Answer 2

to "solve" you need an equation (an = sign)
or to get a number, you need a value for x

Answer 3

1
(((6x - 2) • 2) • (— • x)) • 4
2

Answer 4

3.1 Pull out like factors :

6x - 2 = 2 • (3x - 1)

Answer 5

x
(4 • (3x - 1) • —) • 4
2

Answer 6

2x • (3x - 1) • 4

Answer 7

as phi said, there's no " = " sign, thus, there's nothing to solve

Answer 8

is the question to simplify
\[ (6x^{-2})^2(0.5x)^4 \]?

Answer 9

you should learn a few "rules"

first x^2 (for example) is short-hand for x*x
if we did \( (x^3)^2 \) that means \(x^3 \cdot x^3 \)
also \( x^3 = x\cdot x \cdot x\) so
\[ (x^3)^2 = x^3 \cdot x^3 \\= x\cdot x \cdot x \cdot x\cdot x \cdot x \]
and that is hard to write, so we use the short hand, and write
\[ x^6\]

now notice this "quick way": in \( (x^3)^2 \) 2*3 is 6
it turns out \( (x^3)^2 = x^{2\cdot 3}= x^6 \)

Answer 10

also if you see
(a*b)^2 that means (a*b)*(a*b) which can also be written as a*a*b*b
(we can switch the order when multiplying)
a*a*b*b in short hand is \(a^2 b^2\)

the idea is
\[ (a\cdot b)^2 = a^2 b^2 \]
we can use these ideas to simplify the first part of your problem
\[ (6x^{-2})^2 = 6^2 (x^{-2})^2 \]
6*6 is 36
what is \( (x^{-2})^2\) ?
use the rule up above: it is \[x^{-2\cdot 2}\]
which is \(x^{-4} \)

so the first part simplifies to
\[ (6x^{-2})^2 =36 x^{-4}\]

Answer 11

can you write out (0.5x)^4 ?