Please Help!!? Leah is solving the equation using properties of exponents? 2^2x-3=(1/6)^3x+9
1 answer:
HERE IS HOW TO SOLVE:
Simplify {2}^{2}2
2
to 44
4x-3={(\frac{1}{6})}^{3}x+94x−3=(
6
1
)
3
x+9
2 Use Division Distributive Property: {(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}(
y
x
)
a
=
y
a
x
a
4x-3=\frac{1}{{6}^{3}}x+94x−3=
6
3
1
x+9
3 Simplify {6}^{3}6
3
to 216216
4x-3=\frac{1}{216}x+94x−3=
216
1
x+9
4 Simplify \frac{1}{216}x
216
1
x to \frac{x}{216}
216
x
4x-3=\frac{x}{216}+94x−3=
216
x
+9
5 Multiply both sides by 216216
864x-648=x+1944864x−648=x+1944
6 Add 648648 to both sides
864x=x+1944+648864x=x+1944+648
7 Simplify x+1944+648x+1944+648 to x+2592x+2592
864x=x+2592864x=x+2592
8 Subtract xx from both sides
864x-x=2592864x−x=2592
9 Simplify 864x-x864x−x to 863x863x
863x=2592863x=2592
10 Divide both sides by 863863
ANSWER: x= 2592 over 863
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