Evaluate
\frac{4}{27ab}
Expand
\frac{4}{27ab}
Share
Copied to clipboard
3^{-3}\left(b^{2}\right)^{-3}\times 4a^{-1}b^{5}
Expand \left(3b^{2}\right)^{-3}.
3^{-3}b^{-6}\times 4a^{-1}b^{5}
To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.
\frac{1}{27}b^{-6}\times 4a^{-1}b^{5}
Calculate 3 to the power of -3 and get \frac{1}{27}.
\frac{4}{27}b^{-6}a^{-1}b^{5}
Multiply \frac{1}{27} and 4 to get \frac{4}{27}.
\frac{4}{27}b^{-1}a^{-1}
To multiply powers of the same base, add their exponents. Add -6 and 5 to get -1.
3^{-3}\left(b^{2}\right)^{-3}\times 4a^{-1}b^{5}
Expand \left(3b^{2}\right)^{-3}.
3^{-3}b^{-6}\times 4a^{-1}b^{5}
To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.
\frac{1}{27}b^{-6}\times 4a^{-1}b^{5}
Calculate 3 to the power of -3 and get \frac{1}{27}.
\frac{4}{27}b^{-6}a^{-1}b^{5}
Multiply \frac{1}{27} and 4 to get \frac{4}{27}.
\frac{4}{27}b^{-1}a^{-1}
To multiply powers of the same base, add their exponents. Add -6 and 5 to get -1.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}