+112 Simplify \(^{(x^{25})^{-6}}/_{(x^{-3})^{48}}\).
The power of \(x\) in the simplified expression is \(\boxed{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\downarrow}\).
\(\boxed{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\downarrow}\\ \boxed{-2\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\\ -6\\ -23\\ -26}\)
Simplify the following:
1/((x^25)^6 (x^(-3))^48)
For all positive integer exponents (a^n)^m = a^(m n). Apply this to (x^(-3))^48.
Multiply exponents. (x^(-3))^48 = x^(-3×48):
1/((x^25)^6 x^(-3×48))
Multiply -3 and 48 together.
-3×48 = -144:
1/((x^25)^6 x^(-144))
For all positive integer exponents (a^n)^m = a^(m n). Apply this to (x^25)^6.
Multiply exponents. (x^25)^6 = x^(25×6):
1/(x^(25×6)/x^144)
Multiply 25 and 6 together.
25×6 = 150:
1/(x^150/x^144)
Write 1/(x^150/x^144) as a single fraction.
Multiply the numerator of 1/(x^150/x^144) by the reciprocal of the denominator. 1/(x^150/x^144) = (1 x^144)/x^150:
x^144/x^150
For all exponents, a^n/a^m = a^(n - m). Apply this to x^144/x^150.
Combine powers. x^144/x^150 = x^(144 - 150):
x^(144 - 150)
Evaluate 144 - 150.
144 - 150 = -6:
x^(-6)
Simplify the following:
1/((x^25)^6 (x^(-3))^48)
For all positive integer exponents (a^n)^m = a^(m n). Apply this to (x^(-3))^48.
Multiply exponents. (x^(-3))^48 = x^(-3×48):
1/((x^25)^6 x^(-3×48))
Multiply -3 and 48 together.
-3×48 = -144:
1/((x^25)^6 x^(-144))
For all positive integer exponents (a^n)^m = a^(m n). Apply this to (x^25)^6.
Multiply exponents. (x^25)^6 = x^(25×6):
1/(x^(25×6)/x^144)
Multiply 25 and 6 together.
25×6 = 150:
1/(x^150/x^144)
Write 1/(x^150/x^144) as a single fraction.
Multiply the numerator of 1/(x^150/x^144) by the reciprocal of the denominator. 1/(x^150/x^144) = (1 x^144)/x^150:
x^144/x^150
For all exponents, a^n/a^m = a^(n - m). Apply this to x^144/x^150.
Combine powers. x^144/x^150 = x^(144 - 150):
x^(144 - 150)
Evaluate 144 - 150.
144 - 150 = -6:
x^(-6)
