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16x^{8}
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\left(4x^{5}\right)^{3}\times \frac{1}{4x^{7}}
Use the rules of exponents to simplify the expression.
4^{3}\left(x^{5}\right)^{3}\times \frac{1}{4}\times \frac{1}{x^{7}}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
4^{3}\times \frac{1}{4}\left(x^{5}\right)^{3}\times \frac{1}{x^{7}}
Use the Commutative Property of Multiplication.
4^{3}\times \frac{1}{4}x^{5\times 3}x^{7\left(-1\right)}
To raise a power to another power, multiply the exponents.
4^{3}\times \frac{1}{4}x^{15}x^{7\left(-1\right)}
Multiply 5 times 3.
4^{3}\times \frac{1}{4}x^{15}x^{-7}
Multiply 7 times -1.
4^{3}\times \frac{1}{4}x^{15-7}
To multiply powers of the same base, add their exponents.
4^{3}\times \frac{1}{4}x^{8}
Add the exponents 15 and -7.
4^{3-1}x^{8}
To multiply powers of the same base, add their exponents.
4^{2}x^{8}
Add the exponents 3 and -1.
\left(4x^{5}\right)^{3}\times \frac{1}{4x^{7}}
Use the rules of exponents to simplify the expression.
4^{3}\left(x^{5}\right)^{3}\times \frac{1}{4}\times \frac{1}{x^{7}}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
4^{3}\times \frac{1}{4}\left(x^{5}\right)^{3}\times \frac{1}{x^{7}}
Use the Commutative Property of Multiplication.
4^{3}\times \frac{1}{4}x^{5\times 3}x^{7\left(-1\right)}
To raise a power to another power, multiply the exponents.
4^{3}\times \frac{1}{4}x^{15}x^{7\left(-1\right)}
Multiply 5 times 3.
4^{3}\times \frac{1}{4}x^{15}x^{-7}
Multiply 7 times -1.
4^{3}\times \frac{1}{4}x^{15-7}
To multiply powers of the same base, add their exponents.
4^{3}\times \frac{1}{4}x^{8}
Add the exponents 15 and -7.
4^{3-1}x^{8}
To multiply powers of the same base, add their exponents.
4^{2}x^{8}
Add the exponents 3 and -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}