Exponent Rules
Simplify (3a^2b^-3)^-4
b^12/(81a^8)
Rewrite in exponential form \log_x144=2
x^2=144
Multiply (4.73\times10^(-2))(6.82\times 10^5)
3.226\times 10^4
Expand \log_2(7\cdotx^2)
\log_2 7+2\log_2x
Solve for x. \log(1/1000)=x
x=-3
Simplify x^(3/2)/x^(5/2)
1/x
Rewrite in exponential form \log_(1/2)16=y
(1/2)^y=16
Divide (8.13\times10^6)/(1.23\times10^(-4)
6.61\times 10^10
Condense 3\log_5(15)-4\log_5(x)
\log_5(15^3/x^4)
Solve for x. \log_81 9=x
x=1/2
Simplify ((2a^(-1)b^5)/(4a^4))^3
b^15/(8a^9)
Rewrite in exponential form 3\log_7x=18
7^6=x
Add (7.34\times 10^(-2))+(2.11\times10^(-1))
2.844\times 10^(-1)
Condense 1/3\log x+2\log x+4\log x
\logx^(19/3)
Solve for x. (1/3)^x=27
x=-3
Simplify (1/2x^(-10)y^8z^(1/3))^(-4)
(16x^40)/(y^32z^(4/3)
Rewrite in logarithmic form 12\cdot7^(5x+3)=24
\log_7 2=5x+3
Simplify ((4.78\times10^15)(3.22\times10^(-2)))/(7.58\times10^2)
2.03\times10^11
Expand \log_8((x^4y^3)/z^(1/2))^5
20\log_8x+15\log_8y-(5/2)\log_8z
Solve for x (round to three decimal places). 4^(x+1)=70
x=2.065
Simplify (x^(1/4)y^(-2)z^3z^(1/4))/(x^(3/5)y^(1/2)
z^(13/4)/(x^(7/20)y^(5/2)
Rewrite in logarithmic form y\cdot x^(-2x+1)=y^2
\log_x y=-2x+1
Simplify (5.51\times10^3)-(4.73\times10^2)+(2.23\times10^4)
2.734\times10^4
Condense 1/2\log_3 4-2\log_3 5+\log_3 10
\log_3(4/5)
Solve for x (round to three decimal places). -7\cdot8^(2x+3)=-55
x=-1.005