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# Plato Classroom Question #15

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Simplify $$^{(x^{25})^{-6}}/_{(x^{-3})^{48}}$$.

The power of $$x$$ in the simplified expression is $$\boxed{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\downarrow}$$.

$$\boxed{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\downarrow}\\ \boxed{-2\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\\ -6\\ -23\\ -26}$$

SpaceModo  Jan 24, 2018

#1
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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)

Guest Jan 24, 2018
Sort:

#1
0

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)

Guest Jan 24, 2018

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