indices (O-level revision)

lolaminx SG

hi guys, i'm doing my revision for the topic indices, and i have a couple of questions that i'm having trouble with. hope you guys could help out abit. thanks!

*all questions to solve x.

question 1:

2x to power -3 = 64

Answer is 1/8.

question 2:

3 to power x = 81 to power 2x

Answer is 0.

question 3:

87 to power (2x-5) = 49 / (7 square)

question 4:

x to power 1/3 = 2

*and a small note: i visited maths-tuition.com and apparently, the website is down. just for heads up.

^tamago^ SG

Certain steps seem long for sake of clarity. Skip if you understand the intermediate steps.

4794 SG

question 1, (2x)^-3=64

2^-3x^-3=64

1/8x^3=64

1/x^3=64x8

1/x=8,x=1/8

question 2 3^x=81^2x

3^x=3^8x

x=7x,0=7x than x=0

question 3,i don know lol

question 4, x^1/3=2

x=cube root of 2